Welcome Jim:
Yes, that could be the problem, but water will pump itself if the heat source is below the water in the tub; not as fast as a pump but it will work.
Put a screwdriver end against the circulating pump, put your thumb on the other end and lay your best ear on the thumb. If every thing is on you should distinctly hear the pump rotating (not just an electric buzz).
Then check the connections of all the wires involved, including at the circut breaker in the main panel. One of them might be about burned into. There will be a black patch around the faulty connection so it shouldn't be too hard to find.
Glenn
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