Engine is running rough after blown fuse?

I'm driving an automatic 2001 Mitsubishi Mirage.

About two weeks ago while driving, my car shut off on me. Electrical was fine (battery was replaced less than a year ago), and the engine would crank but not turn over.

After assuming it was a faulty fuel pump or relay, we eventually realized that I had a blown fuse in the engine fuse box (it was a 20A/32V fuse marked with an Engine symbol), and after replacing the fuse the engine started right up.

The only problem is that it's running extremely rough. I haven't taken it out for a test drive, nor do I want to. There's a tapping noise coming from the engine, and after letting it run for about a minute, I noticed a burning smell and a very small amount of smoke coming from the bottom front of the engine. Prior to the car dying on me, it was running just fine with no strange noises or otherwise any reason to think the engine might be in bad shape.

My oil is a bit low and dark (about a third of the way up between the low and high fill lines), and although I intend to change the oil completely this afternoon, I'm just confused here.

What could have happened during/after the car dying that would suddenly cause it to run rough?