Your problem may be different but I had the exact same problem last summer. After much searching I found the bypass valve gaskets had deteriorated over time and the gasket material was blocking the free-flow of water entering the water heater. One of the three was really bad but I replaced all three. Really a simple job. Turn off water, remove the handle and use a wrench, unscrew the valve, replace the gasket then put it back together. The new gaskets can be bought an any hardware store. It's a 30 minute job for a handyman.