89 S-10 Blazer has Electrical Problems - NEED HELP!!!

Hello everybody, I'm a pretty smart guy when it comes to electronics, which can make me very dangerous. I have a problem with my 1989 Chevy S-10 Blazer that I need some help with. Here's the deal...
About 4 or 5 months ago, I started to notice that the battery wasn't holding a charge, and decided I needed to replace it. I was lazy, and didn't do so. Since this was our second car, we only drove it once a week or so, and when we did, we usually had to jump-start it. That worked fine. Last week, I finally decided it was time to replace the battery. I went and bought a new batter, pulled the old one out, and put the new battery in. I connected the new battery and expected to see the under-hood light to turn on... it didn't. That was weird. Well, let's see if it will start. Nothing. Not even a click.
After some diagnosis, I have found a few weird things. First, when I connect the battery properly, I get a perfect 12.56VDC when measuring at the positive (+) battery terminal and the engine block. This tells me that the block is properly gounded. Good. Then I tested at the "terminal block" and the engine block. Nothing. So instead of using the engine block as a ground, I actually put the probe on the negitive post of the battery. Nothing. Okay, so it looks like I'm not getting any positive flow to the "terminal block" located in the back of the engine compartment. I've tried to trace it back, but I haven't done a very good job. Okay, so something is obviously not working right, but what is it?
Okay, so here is where it gets strange (or at least I think it is strange). I decided to disconnect the negative (-) connection to the battery. Essentially, I have the positive side hooked up, and the negative is just hanging there. With this done, I would expect to not be able to get a voltage reading off of anything except for the two battery posts (since the car is no longer grounded). This was not the case. I put the negative probe from my multi-meter on the negative (-) post on the battery and touched the case of the alternator. My multi-meter (DMM) jumped up to 12.56VDC. What? Okay, let's try again. Put the ground probe into the negative post of the battery (but note again that the car frame itself is not grounded) and touched the engine block. DMM reads 12.56VDC. Okay, so now it looks as though my car has changed into a positive ground.
I can tell you where I think the positive flow is coming from... I just don't know if this is to be expected. I believe that the cable running from the positive (+) post on the battery to the post on the alternator is causing the housing of the alternator to be positively charged.
I don't really know what is going on, and like I said, I know just enough to cause some problems. Any help or insight into this issue would be GREATLY appreciated. I am looking to sell this car, and I really need to get it running.
Oh, and one last thing... I quickly mentioned it above, but when the battery is properly installed, absolutely NOTHING works in the car (from an electrical standpoint). Not even the dome light.
Thanks in advance for any help.
Sincerely, Scott Bauer
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