As to the gas side, what you describe sounds like a bad thermo switch. If the thermo switch has failed it will tell the circuit board that the water is already hot, therefore when you turn on the switch inside, the light will not light up as you mentioned. You can check the operation of the switches by just by-passing them. There may actually be two of them the main one is set at 140 degrees and the backup is set for 180 degrees. I believe they are normally closed switches therefore pulling the wires off the back of them and jumpering them together should tell you if the switch it bad. Testing them usually means pulling the switch and putting it in a pot of water on the stove with a thermometer. You attach a volt/ohm meter to the switch set to check continuity and start heating the water, once the water reaches 140 degrees the switch open and halt the flow of electricity through it. If you bypass the switch do so only to test the switch DO NOT leave it this way as it is not safe. These switches will be found under the access cover on the ouside of the rig, they are contact switches which is to say the just sit in contact with the outside of the metal tank. There will be two wires to each one and they may be labled ECO next to them. I will try and get a picture of mine to post showing them if you need it.
Hope this helps.