An outboard hard drive is just a common hd - usually ATA - in a housing with some circuitry for power and to allow it to connect to the computer via firewire or USB. On occasion that housing and/or the enclosed circuitry goes bad.
You can buy these housings for inserting your own hard drive. If the housing (the circuitry) on a preassembled outboard drive goes bad, you can take it apart, remove the drive, and put that old drive in one of the enclosures. If the drive itself is bad, likscrambled, however, that will not help.
Since your drive is usb, there's also a possibility that you're using a driver in your system to control it. Sometimes that driver can go bad due to corruption or updates to the OS. If you've updated both OSX and Windows, there's a chance that the driver, if there is one, could need updating or reinstall. If there's a driver for in on the mac, it should show up in System Prefs, the bottom row "other". Cna't help you on the pc side.
Unfortunately, there are about a 1000 reasons why the drive won't mount. You have to go through a lot a grief to diagnose it.
I'm assuming that the machine will not mount. Have you tried using Disk Utility (Applications/Utilities) to see if it's recognized and it it's repairable?
Using OSX 10.3.9 on a G4