1988 Ford F150 won't start just buzzes?

I picked up this truck to put miles to work and back on. Two weeks after getting it, it started doing nothing but buzzing and draining the battery as fast as I charged it. Come to find out it was a bad alternator. A couple weeks later I replaced the starter. Then the battery. Then it developed a bad miss. I replaced the wires and plugs in in it. Then the wiper switch went out so I replaced it. A couple days after that it started buzzing when I would try to start it. After a few seconds it would fire right up. I noticed that every time it does it, it seems like the battery dies for a split second because my radio resets to AM. I drove it around earlier today. Got in it a little bit ago and it did nothing but buzz and only this time it did not fire up. I'm getting dashboard lights. Radio comes on. Everything but it's just not starting. I did notice a bit of an odor though this time as I cranked it. I'm not very car knowledgeable outside of fairly simple things.

It's a 1988 Ford F150 4.9 Manual Transmission

Any ideas on where to begin?

When you replaced the battery did you clean the insides of the terminals? No I didn't think so. Remove the terminals and look at the burn marks on your new battery. Tighten the bolts this time.