Over time, the little plastic shelf brackets supporting the shelves in our kitchen cabinets have been snapping off, leaving the "peg" part of the bracket stuck in its hole, flush with the cabinet wall.
Previously, I've carefully drilled them out, a PIA job because of their inconvenient locations. One time I got careless, and the drill grabbed and bust through the finished surface of an exposed end panel-Aargh!
Tonight I noticed a heavily loaded shelf sagging in the center and found the bracket on the stile between two doors had broken off. I wasn't looking forward to trying to drill that one out by holding the drill pointing towards me in a spot where I couldn't see what I was doing.
I suddenly got one of my infrequent "aha" ideas, and it worked.
I held a sheet metal screw with pliers, heated its business end with a propane torch, and with SWMBO's pocket mirror in one hand (so I could see where I was) and the pliers in the other, I pushed the red hot screw tip into the busted off plastic peg. It went in like the proverbial hot knife through butter.
A few minutes later the screw had cooled down. I was able to pop the peg out of the hole by pulling on the screw.
File that one away against the time you may be able to use it.
Jeff