I was with Mark trying to get this bike started and the first thing I said was "Fuel, spark and compression and a 2 stroke will start". It had spark and fuel (we ended up putting a few drops down the plug hole to be sure) and it never coughed or even sounded like it wanted to fire. That was why he put the new piston in it - because we assumed that since it had spark and fuel, it must be compression. I'm glad he did replace the piston, as he found evidence of a previous seizure, but it has been running since then, so that shouldn't be the issue. There is also evidence of some serious heat (bubbled paint on the cylinder head) which I suspect was related to the seizure.
I suspect that it's an electrical issue, assuming that the top end was assembled correctly and that the carb was also assembled correctly after cleaning (Mark is experienced with bikes, so this should be a safe assumption).
It's a mystery as to why it is not firing at all, even though it has spark when we kick it over with the plug out?