Hello, & Welcome to Tom's Hardware!
Well, that's an interesting problem. Let's assume the USB flash drive is OK, since it worked on you XP computer. Might just doublecheck that on a separate laptop. Remember that the USB ports may be installed upside down from what you are used to, so check on that also, don't force them.
Then on your 'new' Win-7 computer, go to the BIOS by clicking on 'del' at the splash screen, or equivelent, and go to the Integrated Peripherals page. Sometimes all the USB controllers aren't turned on by default.
Check the SouthBridge or PCH USB controller to make sure that is enabled, and if there are secondary chip controllers or USB 3.0 separate chip controllers if they are also 'enabled'. Look down the list at all the USB controllers. Sometimes the MB maker separates out the secondaryd controllers toward the end of the page. If not 'enable' them, and see if your flash drive is recognized
The USB thumb drives are 'plug and play' so it should be recognized right away.