check sheared key first, replace it if deemed the issue.
Then check carb. Pulsa-jet carb can be taken off (replace 1 diaphram (with spring)) to restore functionality. While you have it off, don't forget to perform a rinse of the tank to rid of debris. Carb hate debris, and these carbs don't have any sort of good debris filtration set up so beware. Get some compressed air (canned compressed air ok) and simply blow clear of all the orifices you have access to (on the carb).
Install it, fill with fresh gas before you try it again.
Lastly: I don't buy that stuck exhaust valve notion. So far, of all the bad (yeah, restore a couple of them that were tossed on the side of the road), and only one of them suffered from a gummy exhaust valve stem (wirebrushed and fine afterwards). That one suffered from severe neglect that I can tell: rancid gasoline, broken(Fallen apart) muffler, no oil change (compression ring a bit word), key sheared,etc. but was still restoratble and now in full service @ pop's place.
If yours was running fine until recently and been properly maintained up and until that point, then I'd keep the "stuck" exhaust valve analysis as the very last one to look for.
Good luck.
Q.