Serious electrical problems I think

Hello out there. I'm new to this area but I already like it. Anyway I own a 1990 Pontiac Sunbird LE and I think I have some serious problems. A couple of weeks ago while I was driving my check engine sign flashed. I was right in the middle of traffic so I ignored it and it eventually went off. Well a week later while I was at church I couldn't leave. The car wouldn't turn over and the radio didn't work. I had it towed and taken to a shop. They installed a new battery so I thought I was straight. That same day my speedometer goes haywire. I mean I would travel a consistent 40 mph and it would jump to like 80. Besides that all the lights would flicker but that's not the worst. I had to brake and it cut off, right in the middle of driving. What the hell! I started it right back up but when I came to a complete stop it was all over. It wouldn't turn over or anything. Went back to the shop and they installed a new alternator. Still the same thing happens. Now I don't really know what else to do. My car is stuck right outside work so at least I can monitor if anyone messes with it. Can someone PLEASE enlighten me on what is the matter with my car? Should I get a diagnostic test done?

Have the computer scanned for codes due to the fact that the check engine light did come on once. I would look at the body control module (BCM) it sounds like it is going bad. They are not expensive to replace and may be the source of the majority of your problems. I would also check the grounds on the car. Bad grounds can do some funny things.