check the head unit holes & pins for corrosion. Make sure the connection is stupid clean.
*I use MAF / electronic cleaner & small fine wire brushes to clean up my junk when it stops wokring.

My Matrix likes a good battery too. I dunno?
I have/ had a love-hate relationship with two Matrix 17...
You may want to save the $85 head unit replacement for the Matrix and get a different unit all together.
$.02
If you were closer I would loan you my head unit to test your connection. Someone local might be able to help?