94 Celica shut off while driving

[wuppy96]

Hello, I am new to the forum, I live in Pennsylvania, and have a 1994 Celica. Two days ago, it just shut off on me right down the street from my house. Right after I had stopped at the stop sign, and stepped on the gas to go, it just died. No noise or shaking, no warning. The only way I realized it was that the power steering went out, and it wouldn't accellerate. I drifted it to the side of the road, put it in park, and proceeded to try to re-start. It wouldn't even try to turn over. All of the battery functions seem to work, windows, lights, etc. The oil light came on when it died also, but it has oil.
First thought was timing belt, but it would at least try to turnover wouldn't it? Checked fuses, all seem to be okay, but on drivers side fuse and relay panel, the cover has been off for awhile, and there was a lot of moisture inside. Does anyone have any suggestions? I'm hoping it's something simple enough to do myself. Thanks.