Here is the deal. The network interface name displays in the output when I enter the "airmon-ng" command if I boot BackTrack from a CD. The moral of the story is to simply not use VMware.
Even after my wireless network card was detected and working beautifully with BackTrack to go online, it still could not be used to crack WEP. I learned that
the majority of wireless network cards can not perform "packet injection" well enough to crack wireless (because the corresponding drivers can not do packet injection). I had to go out and purchase a new (physical) wireless networking card that can do packet injection and reference the
aircrack-ng compatibility list.
Unfortunately, I still did not getting working with my own router but I did a
packet injection test to make sure packet injection worked. The new networking card passed the test and the old one failed, so I am getting closer.