Don’t freak out since you know it’s probably not the flash drive but the other PC since it worked on the original PC. You can test it by trying the drive on yet another PC to make sure the drive works.
I have a feeling that the other PC turned off the ‘Plug and Play’ service in Windows. You can reboot the other PC first and try again. If it still doesn’t work, click on Start, Run… Type “services.msc” into the dialog box and look for 'Plug and Play". Double-click on it and make sure it is set to ‘Automatic’. I had ths problem once but it was because one of my USB ports didn’t work. Try a different USB port too.