78YamahaChappy Leaks/Starting problems.

Here's some more cool pics of the Chappy. Might give you some ideas.
http://www.bikepics.com/yamaha/lb50chappy/

If you can't get that running, Lifan makes a number of replacement 4 stroke motors that you might be able to stick in there. Might go pretty fast with a 140cc motor in it.
http://www.hooperimports.com/dept.aspx?dept_id=02

To troubleshoot:

1 Check the compression. Throttle open wide - no less then 90 PSI; if it's less look first at rings then transfer case seals.

2. Is the carby clean? All the jets clean?

3. Spark? Fresh plug please!

4. Be certain the oil injection is injecting, and not too much.

At 80cc's that engine needs to work pretty much at 100% - especially if you wanna go 45 MPH.

My hunch is transfer case seals or bad rings.

Oh, one other thing - is the exhaust pipe clear of coke? (oily carbon) Someone may have been trying to run motor oil rather than injector oil, this will cause carbon buildup faster that you can say pfft. Pipe service is a requirement on these things.