Yes Robchap, i have to agree with with rusty.ute, it sounds like you've fried the piston and rings at the very least. The excess heat from the exhaust has melted the plastic caused by the the engine running alot hotter than it was intended as a result of the lack of lubrication. I had one with the same symptoms a couple of months ago. once it cooled down, it would run again, and after 15 mins of running flat out would heat up, causing the metals to bind and stop dead and cease up til it cooled down again.
Pull the top cover off and remove the 2 clips holding the muffler. Once off take a look inside and you'll most probably find lots of scoring on the piston and the rings ceased onto the piston. You can check this by pressing on the ring with a screwdriver, you'll find that thre'll be no give as they've locked into the piston.
