I just want to add that this is crappy that the garage isn't being helpful.
I had a similar(ish) situation years ago but it was that my car was stolen while at the dealership for service. They covered a rental car for me immediately (it's what I went home in that night, and I had for over a month), and they covered the car fully. (The one thing they didn't cover, but not relevant to your situation, was the contents of my car. We debated suing for negligence (they'd left the keys in the car and some other things that seemed a bit fishy), but decided it wasn't worth the effort.)
ETA: But, whatever happens, at the end, leave them horrible reviews on Yelp, etc. saying what happened and that they refused to take any responsibility or be helpful.