Q: Electrical issue

My minivan has had some problems since we put a new battery in. Some mornings it starts fine, other mornings it will turn over and then the engine will die and all electronics go out. This includes the icons on the dash, my wipers, lights, blinkers, hazards, everything. Sometimes the power will flicker off and on, other times it just dies completely. After pulling the key out and trying again, it sometimes will happen several times in a row. I have yet to get it to not start after the fourth or fifth try at max. I haven't really noticed a pattern, except I think it might be worse when it is cold, as lately it has been warmer and the van has been better at starting.

Another symptom is that sometimes while driving it will turn off, exactly as described above. Everything just quits. It has only happened when going slow, like after stopping at a stop sign, or on roads with 30mph limits. But I don't want this to happen on the freeway or leave us stranded somewhere.

Thanks in advance

My car has 100000 miles.
My car has an automatic transmission.