Hell of a deal even if it doesn't run imo. I've seen that problem that you described in an e30 and the crank sensor was bad. Sounds like it to me. If it was alt it would never start. Possible bad battery too.
Brake Light circuit error problem - usually caused by bad bulbs or a bad brake switch. Cheap and easy to fix.
Rear Shock Mounts - Cheap parts, but can be time consuming to replace.
02 sensor - Will cause poor idle, bad performance and other problems. 70 dollar part and sometimes is a pain to replace.
ICV - affects idling and accelerating. Can be cleaned usually to fix or replaced for around 100.
Front ball joints - cheap part but a major pain in the arse to replace your self.
these are just a few of the problems I've seen quite a bit.