Run a diagnostic and check which codes you get. Directions on how to do that and what the coes mean can be found here:
http://www.allpar.com/fix/80s-codes.html
Check your cables and wires and fuses and grounding points, yes I know all that is cliche but worth your time to inspect. Also, you didn't specify whether you had the battery tested. A lot of times the battery can be the culprit. I've had my share of electrical problems, and in my case I had somewhat similar symptoms because my battery actually shorted out and fried the alternator along with two 60 amp Maxi fuses. Sometimes idiots testing your system is also a problem. I had one guy tell me my alternator was bad, switched it and said it really wasn't bad, when it really was! Talk about incompetency! All of the electrical is intertwined to form a circuit, and every piece of the circuit is a piece of the puzzle. Sometimes more than one thing could be wrong. Your diagnostic will tell you something for sure, but you can have the battery checked too.