Removal of rusted bolt remains
I have had the same problem and it can go several different ways. 

After realizing the extractor method was not going to work, I resolved to drill it out all the way through and try to chase the threads with the same size tap, to use the same size screw as the original. This has worked, and it has not. It has on occasion, because the hole I drilled was off center a bit, the tap would get the old threads to move, but because of the off centeredness the old threads jammed the tap. That is tedious at best to get through... I also have went the next size up and drilled out the old threads and retapped to the next size up. In some cases going to metric because it "was that just big enough" to get new threads but not so big it messed with the size of the screw head and change things there.

I failed to mention that when drilling out the old screw, combined with the heat generated and the WD40 used, also as typically done when the last bit of metal has drilled through, how the bit grabs the hole and wants to twist the drill out of your hand (with larger holes) or sometime snaps the bit, the short threaded section will dislodge and come out of the bottom of the original tapped hole. That could be good, that could be bad, depending on how easy it is to get the drill back out of the remaining screw.

Now back on track, If all else fails and your framing is wood around the window, run a long enough wood screw with the right sized head and profile to match the others if need be, and get you solid anchoring in the framing under the window jamb.