Modern Vespa

I bought a non-running ET2 50. Replaced stator, spark plug, and ignition switch and got it started and running. It wasn't running perfectly, breaking up here and there, but I just wanted to run around the block to shake it down. It got up to 40 on the speedo and felt ok. Right around the corner from the house, it sounded like it revved out really high and then spun down and sputtered to a stop. Now it won't electric or kick start. Engine turns over and it appears to be flowing oil and fuel. Pulled the cvt cover and it's dirty but the belt is intact and everything spins. Where do I go from here?

Get a compression tester and test cylinder compression. Need 100 psi or higher. Lower means a seized top end/ frozen piston rings.

Sounds like carburetion. Any fuel in the bowl? The rev out might have been as it went lean as bowl emptied and the sputter to a stop and no start is no fuel in the carb.

Haven't pulled the carb and checked yet but there's fuel in the line and it appears to be pulling.

Upon further inspection with a better compression tester, it has about 100 psi compression.

I pulled the carb and cleaned it in the ultrasonic. Reassembled and got it to run but it was puffing lots of white smoke and didn't want to idle consistently. I adjusted the carb and got it to a spot where it was running pretty well and put a few miles on it. Still breaking up here and there and sometimes wanting to idle high when coming to stop. It sat for a day and now will not start with the electric starter or kick start. Battery is now super dead and will not hold a charge. My knee is sore from kicking.

-Has spark.
-There is fuel in the line and pulls when vacuum is applied.
-Has good compression.

What am I missing? Bad kill switch? Bad gas or oil?

High idle points to an air leak.

Air leak might also be the cause of the inability to start - if the leak is causing not enough suction on the vacuum line to the petcock to pull fuel.

I should have explained better - the air leak that mentioned would be at the head or a crank seal. The leak you mentioned would be in a fuel or vacuum line. The white smoke is a symptom on a rich air/fuel mixture. Try a new spark plug, the present one is probably too fouled to work right.

Haven't gotten it to start and run to do a carb cleaner air leak test yet.

But I'm also kind of stumped how it can run rich while also having an air leak that would make it run lean. I'm sure there's an explanation but i don't get it.

It has a brand new spark plug.

I'm a little worried that the person who had it before me used wrong or less-than-ideal oil and it is burning off. I poured in a bunch of good Jaso rated oil to top it off when I got it but based on the color in the oil hose, it has not reached the carb yet.