1997 Hyundai Accent I may have a meltdown. 3 times in a m

Engine Mechanical problem
1997 Hyundai Accent 4 cyl Front Wheel Drive Manual

My car was a very VERY reliable car up until this winter. Since December, my car has stopped working 3 times.

the first time the car wouldnt start. Wouldnt crank. Wouldnt turn over. Tried jumping it. Didnt work. Tried to do the whole pop-the-clutch thing. No bueno. We got a new alternator, and it worked fine.

the second time, I was making a 3-point turn, and it was like it stalled. After that, it made the noise to crank and wouldnt turn over. We found out it was a fuse and the ignition coil (or whatever. Im not very great about cars.) And it worked again.

this is the third time. Yet another problem. Every once in a while, my lights would get brighter, my heater would blow much faster, etc. And then theyd go dim again. I assumed I should get it checked out, but had to wait till payday. That would be today. Now the car wont start. It cranks really really slow. It wont turn over. We tried jumping it. It might have sped up the cranking. But not noticeably, really. Checked the fuses just in case it was burnt out again, they seem fine. Nothing seems to be helping. My only guess is that its a bad battery.

HELP me and my sanity, please!