I hope I could help ,
I have had same type of problems with thing s not working on my cobalt,
start with the bcm fuse s under the hood on the top left side corner you have a 30 amp and a 40 amp ,fuse
all info is on the under side of the fuse box top were every thing is ,
even if it looks ok it may not be ,change it with another fuse and see what happens,
these 2 seem to control the car ,then start with the relays and check every fuse one by one ,it may have come up or is dirty around it ,then go from there .
hope this helps