On Tue, 17 Dec 2013 14:18:25 -0800 (PST), jamesgang
wrote:

You need to use a center punch when drilling out screws. And sometimes you need to start with a smaller bit and then go back with a larger bit.

If the head broke, I'd try a pair of needled-nosed vise gripes.

Or grabits.

•Two-step drill bit and extractor in one tool. Multiple tools not
required.

•Self centering drill tip; no walking or wandering. No grinding,
center punching required.

http://www.amazon.com/Alden-8440P-Grabit-Damaged-Extractor/dp/B001A4CWHO/ref=sr_1_1/178-2073870-2680520?ie=UTF8&qid=1387319797&sr=8-1&keywords=grabit+screw+extractor

YMMV