Well, so far so good. I got the new solenoid installed and took Capri's advice about running a ground wire. I have only started it a handful of times tonight, but so far so good. I will be driving it again tomorrow, so hopefully I have fixed the problem.
btw, I also installed a new 6 piece headlight kit to replace my yellowed ones. Man, they really look sharp next to my new paint! I am turning my eyes toward some Cobra R's now

, but am still debating if I have the money.
Thanks again for your help!