Our hot water pressure suddenly dropped tonight, quickly down to nothing. I shut off the water heater, closed both the hot & cold valves to the tank, turned on the "hot" at a faucet, and tried to drain the hot water tank. I only got 1 gallon or so out of the tank. Does this mean there's a problem with the supply to the tank? Could something be wedge in there? What should I try next?

Thanks for your help!

No, it means that no air could get into the tank so water could come out.

If you want to drain it, close cold water intake open hot water output, open hot water at faucet.

If you want to flush it, (which is probably what you want to do) open hot and cold at tank, connect hose to drain and open drain valve. Let run until clear. If you get no water out the drain or the flow is restricted you have mineral deposit build up in the bottom of the tank. That may be blocking the dip tube and restricting the cold water entering the tank.

Do you have heat trap nipples on the hot and cold pipe at top of tank?