The good news is if your new bike made it to the inspection station and back, it sounds like your engine is runable.
The bad news is I hope you are comfortable working on old bikes, cuz you are going to have to.
You bike loses juice as you ride it likely because it is not charging correctly. You are essentially running on the battery, not the alternator. Ride it long enough and it will stop. This could be as simple as a corroded negative battery cable connection to or it could be a series of connections that corroded from its time as lawn art. Clean your battery cable connections until they are shiny. Then, start the bike and put a mutltimeter between the positive and negative battery connections as the bike is running. Rev the engine to 3,000 rpm and hold it. What voltage are you reading? It should approximate 14.5 volts. If it is less than than you probably will need to clean all the wiring connections. Trace the wires. Clean. Test again.
If, after that, the bike still is not charging correctly, check back here and tell us what you have done and we can be of more assistance.
Before you do anything, though. Get a service manual.
Patrick