Warning lights on. Radio & ac/heat won't come on

Had my parking brake, tire pressure, and door ajar
warning lights all come on at once. My radio and
air/heat won't come on, and my trunk button on my
dash isn't working. We just replaced the battery and
had a shop say that the dealership may not have
synced my battery and the computer in my car,
dealership said there is no such thing. What can be
causing this? Car runs fine after the battery change
other than those issues listed above. Our dealership
is known to have a bad rap for telling people they
need expensive repairs just to get money  as opposed
to the shop that I use is highly reviewed and has
always been 100% honest with their customers. I'm
just hoping for some insight as to what is up with my
car because driving around with no heat in 23 degree
weather is not fun