I whacked a deer on I80 at 65MPH this past march in my itty-bitty Hyundai Accent. Under 4 years old at the time with a 5 year loan. It wasn't pretty, and it could've been so much worse for me and others. So in that sense I felt relieved.
When my head finally came out of the clouds I settled into "worry about money mode". The car had 140K on it and I was sure they'd total it. The estimate came in at just under $6K. The car only cost $13K new. I was sure I was gonna have to eat a big old chunk of that loan. Somehow they didn't total it, and I didn't have to beg or even call them. Was somebody's calculator not working right that day? I dunno, and I didn't ask.
So don't be surprised if they fix it. Used car prices are silly these days, so it just may work out OK. If you can document all the $ you put into it, that may help your case some too.
But if the car was parked and a tree hit it, I'd be looking into homeowners' insurance. Either yours or wherever the car was parked. Not 100% sure, but worth asking.