1990 Lincoln Town Car Car acted posessed and now won't star

I recently (2 months ago) replaced my battery, starter and starter solenoid. Yesturday, all of a sudden while I was pulling up to a red light, my stereo flicked on and off. It kept doing that, then finally just went off. The car seemed to miss a couple of beats in the process, acted almost like when you run outta gas (3/4 of a tank, though). Then it seemed to fix itself and was fine. When I came out of the store, it started up, radio and all. Then, after a quarter-mile it started sputtering again, and finally just died. Now when I try to start it, it sounds normal for the first 1/2 second or so, then I get this aweful ticking noise coming from the solenoid. First I replaced the Altinator (before I realized it was the solenoid making the noise). When I got the same symptoms, I then replaced the solenoid itself AFTER re-installing the old altinator. The altinator was only 3 years old, so I figured I'd put it back in if it wasn't that. So, back to square one. What else would cause this thing to act this way?