The tank eventually stopped firing when water heated up with no new cold being introduced. When I turned the cold input back on then hot water worked in the house, we'll see if it lasts past 50 gallons. My guess is no.
The GE Hot Water Heater Hotline was a complete bust. When completing their test I called back and they guy had no idea what I was talking about. When I asked to be transferred to the gal that was previously helping me he got fairly rude. He put me on hold for a long time, and then told me I needed to test the temperature with some thermometer I'm supposed to have handy. Well, I don't have one handy and he thought that was pretty ridiculous. I just told him I'd call back after I go buy one. I won't be calling back. If the water runs cold after 50 gallons I'll call a real plumber. Thanks guys for all your help.