Help with stripped screw head

Hi gang,
Last night it became apparent that the two 6922's in my cd player needed replacing. Having a pair on hand I decided to have at it. My player, a Tube Technology Fusion CD64 has a wrap around cover that slides off. One of the screws on the underside that takes a standard small phillips head is totally stripped. Nothing will work, I've tried 6 different screw drivers, an allen wrench, and needle nosed pliers. That head is totally stripped and nearly totally flush with the chassis. I'm sure there are ways to deal with this but I'm not at all technical, I just want to do this withour destroying the chassis. Help?
You can get a small screw extractor from Sears (for example) which you attach to your drill and it will allow you to just back the screw out. Its designed for stripped screw heads.
The Sears extractor set worked perfectly for me in an identical situation.
File a slot across the head and use a slot head screwdriver.
Screw extractors as mentioned. Sometimes they are referred to by the name, "easy-outs"
If you can get an appreciable hold of the screw you can try a diagonal cutting tool to grip the outside of the screw head. The longer tool the better (6"-8") to provide adequate torque.

Diagonal Cutting Tools
If you can get a hold of the screw head, a pair of needle nose vise grips should do the trick.
I want to thank everyone. At your advise I went out and got a srew removal bit for my drill and mission accomplished. Thanks for the advice, you guys always come through in a crisis.
Not sure the Sears will be small enough though.Plus never goes on sle.Can get it for half price (half of $20) if you open charge account.