The broken bit is probably HSS , so you need something harder, and there aren't many things harder that aren't also expensive ;P
However, I have had good luck drilling out buts using an ordinary carbide masonary bit. Keep it wet or oiled (water is probably better for cast) and don't push it too hard or it will wander.
Drilling cast iron is a problem in it's own right, it often has sand in it, and it expands while being drilled and grabs the drill. go slow, keep the bit lubed, and expect to use several bits going that deep. ...
If money isn't an issue, diamond point bits are available, they use them for glass and tile, and they will drill HSS , same thing tho, if they get hot, the bonding material will fail. (Masonary bits will fail if the bit gets over 400 degrees as the solder melts and the carbide falls out)
As an aside, it was probably obvious to whomever demilled that thing that all you would need to return it to service is a drill bit, so don't be surprised if there is more to it than drilling a hole...(could be a rock in there, or a hardened steel sliver, who knows)
2c
PS: I hope thay aren't planning on putting much power in this thing ;P
