You could do a range check on the radio.

Antenna down, put the buggy on something to hold it off the ground and walk away and see how far you get.

With no other interference from other radio etc you should get 10ft or so.

If it all works the radio is probably ok.

More than likely the main battery in the buggy doesn't have enough real power to supply the motor and radio under load (It is old right?). The radio usually looses out and the buggy will still run just not very fast.