hmmm, KOMODO had a problem very similar to this a little ways back, but he had blown alternators, and have a ton of electronics in his car.
My initial guesses would of course be to check the battery, see if the starter needs replacing, check the alternator, check the alternator cooling duct. beyond that i have no idea.
and welcome to the forums!
I am transfering this thread to the e36 forum however where it belongs and will get the proper attention.