On the Linux Compatible.org, it is stated that the F5D7050 Belkin Wireless G Adapter will work right out of the box so I went and bought the adapter. It works fine with Windows XP, but Ubuntu 8.04 doesn't recognize it. I'm running Ubuntu off a CD; it's not installed on my hard drive.

I'm definitely no expert on Linux or wireless systems. Does this look like an incompatibility problem with the Adapter or is it something else?

Any help will be appreciated!!

What version of the device are you using? There are five different versions, some have different chipsets. This may be the source of your problem. Note that the person who posted on the compatability database gave the FCCID of the unit that he had. In his case, he had version 4, which I will guess had a ralink chipset, which would explain why it worked in Ubuntu.