I've has success removing "easy outs" after they've snapped off. I use my Dremel and set it up with a very small collet and dental burrs - ask a dentist if he can give you some of his burrs that are not good enough to use on teeth anymore. Wear safety glasses, and on high speed, work your way tightly around the easy-out, a little at a time, and use a light oil to lube the burr from time to time. Just keep at it, around and around the easy out. At some point the easy out will move, and you can use needle nose pliers to pull it straight out.
Then, now that you have a nice hole in the top of the bolt, use a left-hand drill bit - one that drills in reverse - to slowly enlarge the hole in the bolt one size at a time. One of two things happens, the broken bolt suddenly spins out - that's why you're using a left hand drill bit, or when you look at the bolt hole before drilling in with the next size drill, you can see that you've started to drill into the threads of the hole in the block. At that point, you should be able to pick at the edge of the bolt with a very small chisel, and carefully curl that edge in towards the Center of the drilled hole, which effectively reduces the diameter of the bolt and loosens it from the threads so you can remove what's left.
Check the threads in the block for damage, re-tap to clean them up. Takes a lot of time and patience, but I've removed a lot of snapped-off bolts that way. If the threads are damaged, you can use Helicoils to bring them back to the original size threads in about 5 minutes or less. Good luck!