Modern Vespa

Hello, all! This is my first post so I'll try to make it as to the point as possible. Thanks in advance for any help you can give.

2012 Piaggio Typhoon 125
518 miles

-Scooter with 400 miles sat for a few years unable to start.

-Changed spark plug and back to life

-Scooter fell on air filter side while accessing spark plug

-After first test run saw white smoke for 15 seconds after shut off on cold rainy day, no smoke since

-Successfully drove to and from work a few times, sudden loss of power while accelerating, scooter would not restart.

-Carb cleaner added, driven for a bit, allowed to idle for 25 minutes to get carb cleaner working

-drove a few more times

-Car pulled out in front of me and I laid scooter down again

-start to drive home, loss of power again and no restart

-check air filter, full of oil

-clean out air filter bike comes back to life but seems like may still be getting oil in air filter

-noticed a smell like burning rubber today

-currently monitoring situation

I'm hopeful I'm not truly having blow by, but in the event that I am, I can't seem to get my hands on a good guide or anything with pics/video of step by step instructions for tracing it and accessing the engine if necessary. Does anyone have any tips?

Oil in the air filter is expected if the bike has been on its side. So no immediate cause for panic on that point.

It's quite possible that the bike will recover with some additional attention to the air filter as the residue continues to work its way out.

That said, some oil will occasionally migrate to the air filter even without a tip-over, so I still wouldn't panic if you continue to get a small amount accumulating.

If the bike resumes running and you aren't seeing additional smoke out of the tailpipe, I think you're probably okay.

Oh, and definitely top up your oil after the tip-over.