2001 Dodge Grand Caravan electrical problems when cold

I was given a 2001 dodge grand caravan SE last april, knowing that it had many kms and some issues to begin with. Engine is great, starts when very cold with no issues. Was having problems with heater not blowing hot air and started overheating the engine so I replaced the thermostat, and have that in working order now. However a new problem has developed.

Now when the temperature outside reaches -25 and colder, the electrical console in centre does not work when engine is running. Altogether, the windows, wipers, radio, defrost, heat/fan, and clock do not work when this happens. It turns on when I have the engine off but key in ignition however.

I let my fan run yesterday in between stops in an attempt to defrost some of the windshield, but it drained the battery and I needed a boost to get it started again. Battery posts were corroded and someone suggested the battery might not have enough charge to run everything (had it die once during summer when playing the radio with engine not running so figured might be part of it). Replaced the battery but electrical stuff still does work in cold. The kaltire guy said maybe it was alternator?

I do not want to put in a bunch of cash fixing up an old (free) van, but if I could find a simple solution to last the winter that would be great. Perhaps a fuse connection? I need some suggestions on what it could be and whether or not it is even worth persuing trying to fix.