Yeah, I'd suggest *not* cashing or depositing their check, too. Doing so might signal your acceptance of their "offer" and might make it impossible for you to pursue fairer compensation.
They should have talked with you and come to an agreement before sending you any form of payment. No way they can just arbitrarily decide an amount and send it.
They should simply pay whatever it takes to put the car back into the condition it was in, before the accident. You can get estimates from repair shops yourself, maybe two or three, to better know what to ask for.
If it were me, my next step would be to politely decline their offer (check) in writing and present those actual repair estimates. If that didn't work, it things would start getting less polite!
Your insurance company should go to bat for you. If they don't, you might need to hire an attorney to send a letter. Alternatively, you might be able or take it up in small claims court eventually. However, before going to the expense of an attorney or court, there may also be an insurance commissioner or board in your state where you can put some pressure on the company. Also, sometimes a local district attorney's office has a division relating to insurance and auto repair issues.
Insurance companies have a bag full of tricks they like to use to try to reduce what they pay out, and probably get away with it more often than not. But, they make mistakes too. Some years ago, after an accident in which the other driver was quite clearly at fault (arrested and ticketed), his insurance company representative asked me, "Was he drunk again?". He was, but she should never have let me know this wasn't the first time. I started seeing lots of dollar signs and thinking about "pain and suffering" lawsuits, but ended up reining myself in and getting fair replacement value for my totalled car!
/ubbthreads/images/graemlins/cheers.gif