Any noticeable impact when the drive is powered up is a Very Bad Thing, I'm afraid to say. I suspect you had a head crash, with the electronics still working (so it's seen by Windows), but damage to the heads and/or data means it can't read data when it's requested.
These drives have several heads flying close to fast-spinning platters, each is like a 747 flying at top speed an inch off the ground. The heads are "parked" when the drive is off - I have a 80GB 2.5-inch USB drive, which has been stuffed in bags and pockets, but only when off. It once fell about 5ft on to the floor, and it's still working.
The 350GB size means yours must be a 3.5-inch drive. Can you see any external damage on the case? I don't know exactly what you have, or its caddy, so it's hard to say, but unless you know what you're looking for, I'd avoid trying to open the caddy without talking to the maker. But it doesn't sound good.
