Thanks Dirty30 -
Moped Army comes up quite a bit in google search results for Amstar Nostalgia problems, so I thought I would try here.
I used the multimeter on the battery, and the battery appears to be pulling current.
The solenoid isn't clicking at all anymore. The lights turn on, but when I press the electric start nothing happens. I tested the resistence and it shows OL - I used a screw driver to try and bypass the solenoid but it didn't do anything.
I can't find any damaged wires. Any idea what else I could check?