What is wrong with my 3000gt?

I have had my 3000gt for a little over a year now. It has 90k miles on it.. when I bought it, it had 60k. After having it for a month the transmission blew out. I put a brand new transmission in it. Then a few months later the alternator went out, or so I thought... I took it to the shop and they said it was fine and they had to connect some wires... After that I was ran off the road by an SUV and hit a curb and bent one of my rims.. Anyways.. now my car shakes violently.. I've had it aligned, there are BRAND NEW tires on it, that have been rotated... The oil has been changed... but it still shakes.. mostly when I accelerate or go up hills. It stops when I take my foot off the gas, and drives normally unless I give it too much gas. When I take the overdrive off it drives a little better (doesn't shake AS much) . I'm having my alternator replace at this moment because it finally went out. What could it be?