Alright guys ... need your expertise now more than ever...
I have a couple of problems with my 96 Corolla1.8
I live in chicago and its extremely cold out(problems happen only in cold)
Couple of days ago i was driving to work and my battery light tuned on... my steering wheel locked even though the car was still running. I stopped and turned the car OFF and back ON and battery light went away and car behaved fine again. Today i was going out and tried to turn my car on and no lamps came on steeringwheel was locked up and the transmition could not be moved even with the key in the slot and transmition unlocked...
I jump started my car thinking it was dead and it turned on again just fine...
I went to my friends house (30min) drive, and when i was leaving about 3 hours later my car wouldnt start again???
does the steering problem have anything to do with batter or not really?

I though either the battery wont hold the charge or the alternator, please help me hunt this problem down...
TIA, Ed