what a b!tch of a thing to happen!!
this is one of those situations where the golf course
morally has an obligation to pay you, but
legally it's a grey area (it's really up to you to fight it)
getting a lawyer to write a threatening letter is not a bad idea, but lawyers charge like a wounded bull for these things and a lot of times it goes nowhere, because the party you are claiming against knows you're just blowing a lot of smoke up their ass, that you aren't really going to get your lawyers on to them
julie had a good suggestion about goint to your insurer although depending who your cover is with, you will have varying degrees of success. the other thing is you will probably to pay some sort of excess if you claim through your insurer, and if you don't claim they probably won't be interested in coming into bat for you... [edit: i reread your post and just realised that is exactly what
did happen when you called them!]
personally i would go with what goombeast said about lodging a small claims complaint - just remember the process differs from state to state so you need to check out what the process is for your state - this is also likely to be the cheapest option, and why should you be out of pocket for something that isn't your fault and you have no control over?
anyway good luck, and let us know what happens