I was changing the thermostat in my caprice (second repair it has needed in the year ive owned it) and for some reason one of the two bolts that holds down the gooseneck was increadibly tight. After trying for awhile I finnaly snapped the head off. Now the gooseneck isn't tight enough and it leaks, badly (of course). So it is currently undrivable, what I am wondering is HTF do i get that bolt out of there so I can put a new one on?

I did this once. I believe the solution was to drill the end of the broken bolt with a dremmel tool so you could use a screw driver to get it out.

problem is, even if I could get a screwdriver on the bolt I dont think it would come out... its in there very very very good

Not even with an electric screwdriver?

You want to drain some of the coolant. Stuff a rag into the hole for the t stat, then usie a punch to give yourself a centered divot and drill the bolt with a drill (Oregon members...I tell ya). Then..use a reverse thread extractor to remove the bolt. I have had to drill very close to the threads in order to relieve pressure and get the old remains out. If necessary you can as a last resort drill fully and put a helicoil in the hole to rethread it.

Get you a can of PB Blaster (penetrating oil) and spray some of that on there too, before you use the EZ-Out (screw extractor).