So, you bought a "new" HDD without packaging and have no idea what brand and model number it is? There's no markings anywhere to signify the model number? Any reputable hard drive maker will indicate this very pertinent information somewhere, in addition to all the stampings of approval from various authorities (UL, CE, FCC, etc). Either the seller stripped off the placard or put the drive in a generic casing, both of which raise the suspicion meter into the uneasy zone. FWIW, I recommend you stick to brand new sealed package HDD's in the future. It brings a peace of mind as well as the recourse to return it or get warranty service. With this particular HDD, you may not even have the chance to return it to the eBay seller if it is established that it is faulty.

If your Vista installed computer has a history of not recognizing other devices, this compounds the problem. But, you say that the HDD worked only for a few minutes in W7 before it ended up "rejected" or not recognized. Maybe you have a bad USB cable. Try swapping that out and getting the HDD to work on your W7 machine before anything else. You want to establish that it's a functioning device before dealing with the problem child Vista computer.

Finally, be sure you've applied SP2 (service pack 2) to Vista and run Windows Update to get all of the latest updates. Earlier versions of Vista had device driver issues that were rectified in SP2 and later.