I have an allen key bolt that is keeping the 4G transmission hooked up to the old motor and I can't get it out.
Hey Hawaii,
I had a similar problem YEARS ago. Took the part to a mechanic and he looked at it and said "If this was Africa and that was a baby, we'd have to kill it"...but I left it with him and he got it out though never told me how.
Anyway, you mentioned breaking 2 drill bits so I'm assuming it's a hardened bolt you're trying to extract and I'm guessing it's located in a place where you can't get vice grips on it. Here's a couple of things you can try.
Try hammering in a Torx or Robertson drive (it's a square shape) until it gets a bite then use an impact driver with a socket that fits the bit you drove in. Since it's an allen bolt it might be best to use the kind of impact driver you hit with a hammer. The force of the hammer will help keep bit in the bolt as it turns the driver to reverse the bolt out
You might also try grinding down the tip of a regular old screw extractor until it can get a bite then hammer it into the bolt until it has a good hold and also use the impact driver.
When heated, aluminum will expand more than steel. If you have a torch available, heat the area just before you hit it with the impact driver. You don't need to get it so hot that things start smoking, just warm it up until it's hot to the touch.
If none of these work I have more things you can do.