Could be alternator, battery, DME, regulator, etc., etc.
What does your voltmeter show (the gauge on the far right of the dash gauge set)? Has that reading changed recently?
A wild guess is to take your spare (and known to be good) DME and swap it with the one in your fuse box and see what happens. Takes 5 minutes. Wait, you said it didn't crank? If it cranked and didn't start, I'd try the spare DME.
Because you said it wouldn't crank, but then 5 hrs later it cranked and ran fine: If the battery was dead and you didn't charge it, this points away from the battery and charge level. Could be a bad battery cable that as it gets hot, resistance increases and the electrons can't get through. Unlikely, but possible.
A competent mechanic should be able to troubleshoot it fairly easily.
Oh, and glad you are ok after losing the power steering mid-turn.