Does anything else connect to your usb port?
Don't forget that once you connect your PC to the PSP using the USB cable that you need to go under the system folder on the PSP and initiate the USB mode.
If that doesn't work then it sounds like you need to update your usb drivers...
if you press:
1. <windows key>+<pause/break>
2. Click on the "hardware" tab
3. Click "device manager"
look for any yellow exclamation marks... they normally mean the drivers aren't correctly installed OR you have a hardware conflict (not common anymore with computers not having any ISA slots in em).
If there ISN'T any marks on your usb drivers, the next step is to try plugging your psp into your friends computer.
If it works there then your USB drivers are either still suffering crappy/missing drivers.
If it doesn't work, then your usb cable may be bad, OR your psp's usb output is shot... send'r back to Sony.