[cart around]

I think the first suspect is the battery.

After that there is a corroded, or loose connection.

Telltale sign is radio would not work, but does after pushing. Pushing the cart either gave the battery time to come back up a little for the radio to turn on, or bounced the cart around enough to barely make the connection which allows the radio to work.

First step is to load test the battery. After that, start cleaning all connections.