Being that you found water in the burn chamber I agree with the other plumbers that believe the tank is leaking. Tanks can leak a little them stop....this cycle could continue for a while before it totally fails and really leaks alot of water.
There is a chance the water you found in the burn chamber could be condensation and your heater is not leaking.
The T&P valve probably stopped relieving itself because the water heater shut itself down when the pilot went out and the tank went cold.
If its condensation you will not find more than a quart of water max around the heater.
I advise you to find a reputable plumber and trust his judgement because without being there its very difficult to have a real opinion.
Your T&P valve discharge line should terminate outside in Florida.