If you managed to push (bump) start the car, then the battery had enough voltage to power the ecu and ignition coils, but not enough to start the car or operate the power steering.
You may find if you drive it for a few miles, then all will appear well again.
If this is the case, then in all likelyhood, the alternator is fine, but the battery has had it.
This time of year is the toughest for car batteries.
I'd have the battery and then the alternator checked out as a first port of call.