Dropped this camera. Can not get the batteries out. suggestions are h

I suspect you may have to force it which will risk doing further damage. If you can work out what's stopping it opening you may be able to minimise the risk. I've uploaded 3 pics of the battery compartment door which may help you work out what's wrong. First thing is to look for any visible distortion of the body or door which is causing it to jam.

In order to open the door you slide it outwards (1st pic). Is this what you can't do? You may be able to apply more force by inserting a spudger or thin blade of some sort in the crack between the door and the body at the hinge end.

The 2nd pic shows the mechanism with the door open. The plastic door is screwed to a piece of metal which slides on a second piece of metal which forms the hinge. Something here may be distorted, but unless the plastic door is broken it seems not very likely.

The door latches closed at the silver end, on one side just by the brown battery retainer (3rd pic) and on the other just inboard from the black screw you can see. Again, I don't quite see how this could be a problem, but you could try removing the 2 silver screws under the AV cover. This should give a little play in the silver end piece, but try not to force it as it's still retained by the black screw visible in the 3rd pic.

If the camera is otherwise functional but you have a broken case you can pick up a "spares or repair" one on eBay - they appear now and then and go for £10 - £20, and follow my disassembly guide Disassembling Canon PowerShot SX200 IS to swap the cases.