Thanks for the responses, everyone :-)
Broken garage door can be a safety issue - if it's not secure someone can break in, etc.
I wouldn't necessarily stay away from the home. I'd first find out why it's being sold that way, is the seller just in financial distress? And can you back out if you're not happy with the home inspection? You also need to find out what you have to lose. In my state, the only thing the buyer stands to lose in this situation is the home inspection $$ & their time.
Not being from your area, I'm not sure if that clause it binding (it would not be here in the Chicago area)... here, you could still ask, and they'd be within their rights to decline.