Sulphur Smell
Sulphur Smell
If you could smell sulphur when you opened the door, it's likely to be coming from the front of the car, not the back.
Sulphur smell is likely to be cooked off from Sulphuric Acid in the battery.
If your Alternator has gone TU or the battery is old, in this weather you're going to be making big demands on what is left of the battery (lights, heater etc)
If the electrolyte is low or frozen, then the battery is going to struggle and will give up the ghost.
I've seen a dead battery in a car get jump-started by a slave sat on the pavement, only for the slave to explode. All leads hooked up right, but after 2-3 seconds of power demand on the slave, it simply exploded! Plastic and acid all over my Dad & the 4 cars parked nearby which needed hosing off.
If you've got no electrics, you won't have any spark causing rough running (2 or 3 cylinders) and loss of power
A Battery is a lot cheaper than a cat, but an alterator can be cheap too - or pricey depending on the car.