Ok, so here's the scoop. I got the old starter out!

I used the 8mm Allen socket you guys suggested and a lot of pent up anger, and got all the bolts off. There were two connections to the screw on top of the solenoid, and one to a tab on the solenoid. One wire was attached to the screw on top of the starter housing. Anyway, I took it all off, and cleaned all the contacts. The screw on top of the old solenoid was loose, perhaps indicating that the connections inside were not great, but whatever, I just put in the new starter. I put the connections back and tightened everything down, checked the voltages, and tried to start her up. IT WORKED!!

Well then I grabbed all my stuff and cleaned up and turned off the car. Just for kicks and giggles I tried to restart the car....ONE CLICK!!!

What is going on here?!? Could I have put the electrical stuff back on wrong? I doubt it if it started the first time. I thought that maybe I could have drained the battery even though it was reading 12.48 V, so I tried to jump it with my Honda, but nothing happened. Do any of you have any ideas what could be going on? I was going to be all excited about telling you my car works, but alas I have been thwarted once again. Let me know what you guys think when you get the chance. Again I appreciate the help.
Jonathan