Hey Robert,
It sounds like it may just be a loose connection. But to fix it - it requires a bit of work. See, inside the desktop those USB ports tie together and plug into a USB hub inside the system. Either a HUB has failed / is failing, or the cable connecting the HUB to the USB ports is loose. I'm going to use less technical - more generalized terms below because the theory is more important than the terminology.
Because its a desktop:
Step 1 - Power down and unplug the unit
Step 2 - Open the case - do not touch the insides
Step 3 - 'Ground' yourself (ie: touch your house heater vents). This is to discharge static (or you may damage one of your PCI cards / mother board through a static discharge. Usually the harddrive controller card is the first to die in the chain)
Step 4 - Trace the cable running from the front USB ports to the Motherboard
Step 5 - Check how well 'seated' it is. Make sure it is plugged in. And worst case scenario - unplug and replug it in.
Step 6 - Reverse the steps and test the USB ports
Problem still occuring?
Step 1 - Repeat the steps above, opening the case and discharging static again.
Step 2 - Follow the rear USB ports to the motherboard. They should plug in beside the front USB ports. Swap the two and pack the unit back up.
Step 3 - Check if the ports work and if the rear ports work.
If the front USB ports still dont work (and the rear ones still do) you know the ports on the front of the unit are faulty! You might need to replace them with new ones from a part supplier (like www.tigerdirect.ca)
If the front USB ports work and the rear one now doesnt - you know to suspect the location you are plugging into. Check how many slots you have for USB devices on the motherboard. See if the USB ports are plugging into a modular (replacable) unit.
That should at least help you isolate where the fault lies.
[Edit] Another quick tip: Check your Windows Device Manager with a device plugged in. This can provide a little bit of cryptic information in some cases. If nothing is listed at all when you plug in the unit - it is a 90% chance the front USB drives are just unplugged. If it says a device has failed or is not recognized - it could be a failure in the hardware.