We got the install done, but there were two issues that did not get resolved.

1)  The xfce desktop menus were hidden and so were all icons.
Solution:  Install xf86-video-ati

2) BCM4321 wifi interface not workig.
Solution:  Install b43-firmware (From AUR)

After solving the above two issues, the HP-6715b laptop has a shiny new Arch Linux Operating System that seems to be fully functional.
(Using it now to write these notes.)

So here are the install instructions from the official Arch Linux "Installation Guide" I'll try make notes and/or edit out the steps that we can skip and add in a few notes that will help [any of us] with the next Arch Linux install.   (From:  https://wiki.archlinux.org/index.php/installation_guide )
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Arch Linux should run on any x86_64-compatible machine with a minimum of 512 MB RAM. A basic installation with all packages from the base group should take less than 800 MB of disk space. As the installation process needs to retrieve packages from a remote repository, a working internet connection is required.

Download and boot the installation medium as explained in Category:Getting and installing Arch. You will be logged in on the first virtual console as the root user, and presented with a Zsh shell prompt; common commands such as systemctl(1) can be tab-completed.

To switch to a different console—for example, to view this guide with ELinks alongside the installation—use the Alt+arrow shortcut. To edit configuration files, nano, vi and vim are available.

Set the keyboard layout

(We skipped Setting the keyboard layout because it is US by default so I deleted this section.)

Verify the boot mode   (We skipped the UEFI issue because the laptop was pre-UEFI)

If UEFI mode is enabled on an UEFI motherboard, Archiso will boot Arch Linux accordingly via systemd-boot. To verify this, list the efivars directory:

# ls /sys/firmware/efi/efivars

If the directory does not exist, the system may be booted in BIOS or CSM mode. Refer to your motherboard's manual for details.

Connect to the Internet

The installation image enables the dhcpcd daemon on boot for wired network devices. The connection may be checked with:

# ping archlinux.org

If no connection is available, stop the dhcpcd service with systemctl stop dhcpcd@, Tab and see Network configuration.

For wireless connections, iw(8), wpa_supplicant(8) and netctl are available. See Wireless network configuration.

Update the system clock

Use timedatectl(1) to ensure the system clock is accurate:

# timedatectl set-ntp true

To check the service status, use timedatectl status.

Partition the disks

When recognized by the live system, disks are assigned to a block device such as /dev/sda. To identify these devices, use lsblk or fdisk — results ending in rom, loop or airoot may be ignored:

# fdisk -l

The following partitions (shown with a numerical suffix) are required for a chosen device:

Swap space can be set on a separate partition or a swap file.

To modify partition tables, use fdisk or parted. See Partitioning for more information.

If you want to create any stacked block devices for LVM, disk encryption or RAID, do it now.

(We used a test fdisk’s own partition tool to calculate how much to leave at the end for swap - we set swap at the first of the drive and the other partition at the end and used the size of the last partition to recreate the first one - after deleting the partitions and starting over, we knew what size the / partion should be to leave 4G at the end – in other words, we wiped out the partitions and started over with the / partition first and swap last.)

Format the partitions

Once the partitions have been created, each must be formatted with an appropriate file system. For example, to format the root partition on /dev/sda1 with ext4, run:

# mkfs.ext4 /dev/sda1

See File systems#Create a file system for details.

Mount the file systems

Mount the file system on the root partition to /mnt, for example:

# mount /dev/sda1 /mnt

Create mount points for any remaining partitions and mount them accordingly, for example:

# mkdir /mnt/boot
# mount /dev/sda2 /mnt/boot

genfstab will later detect mounted file systems and swap space.

Installation

Select the mirrors

Packages to be installed must be downloaded from mirror servers, which are defined in /etc/pacman.d/mirrorlist. On the live system, all mirrors are enabled, and sorted by their synchronization status and speed at the time the installation image was created.

The higher a mirror is placed in the list, the more priority it is given when downloading a package. You may want to edit the file accordingly, and move the geographically closest mirrors to the top of the list, although other criteria should be taken into account.

This file will later be copied to the new system by pacstrap, so it is worth getting right.

Install the base packages

Use the pacstrap script to install the base package group:

# pacstrap /mnt base

This group does not include all tools from the live installation, such as btrfs-progs or specific wireless firmware; see packages.both for comparison.

To install packages and other groups such as base-devel, append the names to pacstrap (space separated) or to individual pacman commands after the #Chroot step.

Ok, instead of just the above command, we did a lot more:
# pacstrap /mnt base grub networkmanager network-manager-applet xorg xfce4 xfce4-goodies alsa-utils udisks2 firefox sddm

Configure the system

Fstab

Generate an fstab file (use -U or -L to define by UUID or labels, respectively):

# genfstab -U /mnt >> /mnt/etc/fstab

Check the resulting file in /mnt/etc/fstab afterwards, and edit it in case of errors.

Chroot

Change root into the new system:

# arch-chroot /mnt

Time zone

Set the time zone:

# ln -sf /usr/share/zoneinfo/Region/City /etc/localtime

Run hwclock(8) to generate /etc/adjtime:

# hwclock --systohc
We could not get hwclock do do anythig so we just skipped it - all is well... 

This command assumes the hardware clock is set to UTC. See Time#Time standard for details.

Locale

Uncomment en_US.UTF-8 UTF-8 and other needed localizations in /etc/locale.gen, and generate them with:

# locale-gen

Set the LANG variable in locale.conf(5) accordingly, for example:

/etc/locale.conf
LANG=en_US.UTF-8
We did:
echo LANG=en_US.UTF-8 > /etc/locale.cof

If you set the keyboard layout, make the changes persistent in vconsole.conf(5):

/etc/vconsole.conf
KEYMAP=de-latin1

Hostname

Create the hostname(5) file:

/etc/hostname
myhostname
We did:
echo HP-6715b > /etc/hostame

Consider adding a matching entry to hosts(5):

/etc/hosts
127.0.0.1       localhost.localdomain   localhost
::1             localhost.localdomain   localhost
127.0.1.1       myhostname.localdomain  myhostname

See also Network configuration#Set the hostname.

Network configuration

The newly installed environment has no network connection activated by default. See Network configuration#Network managers.

For Wireless configuration, install the iw and wpa_supplicant packages, as well as needed firmware packages. Optionally install dialog for usage of wifi-menu.

Initramfs

Creating a new initramfs is usually not required, because mkinitcpio was run on installation of the linux package with pacstrap.

For special configurations, modify the mkinitcpio.conf(5) file and recreate the initramfs image:

# mkinitcpio -p linux
We skipped this mkinitcpio step

Root password

Set the root password:

# passwd

Boot loader

See Category:Boot loaders for available choices and configurations.

We istalled grub as our boot loader so we did this:

# grub-install /dev/sda
# grub-mkconfig -o /boot/grub/grub.cfg

If you have an Intel CPU, install the intel-ucode package in addition, and enable microcode updates.

So before rebooting, we went a step further and created the user and added him to a bunch of groups and set password for user:

# useradd -m -G wheel,video,audio,scanner,network,optical joe 
# passwd joe  
   type password 
   again…
So we went another step further and enabled the NetworkManager and the login manager
# systemctl enable NetworkManager
# systemctl enable sddm

Reboot

Exit the chroot environment by typing exit or pressing Ctrl+D.

Optionally manually unmount all the partitions with umount -R /mnt: this allows noticing any "busy" partitions, and finding the cause with fuser(1).

Finally, restart the machine by typing reboot: any partitions still mounted will be automatically unmounted by systemd. Remember to remove the installation media and then login into the new system with the root account.

We did not login to the root account because we had already created the user and had the login manager enabled.
Basically, we had already accomplished the post-install tasks and so we were pretty much finished when it came time to reboot.
….Accept for the fact that we needed the ATI video driver and firmware for the BCM4321 wifi interface.