My KRV-7070 shuts down when it gets too hot. It is either off or on, so your problem is interesting. You didn't mention whether the receiver's built-in fan was working. They can fail, as can the circuitry that turns them on. Also, check that the 8 ohm/4 ohm switch is in the proper position. Finally, make sure there is adequate ventilation around the receiver. Nothing should be placed on top of it. In fact there should be at least a couple of inches above it, on both sides and behind.
The touch dimmer module is an easily replaceable part, available for less than $10 at Home Depot and other home repair stores. Replacement instructions are included with the part. Depending on the lamp, tools involved are very simple. The wiring is usually connected with simple plastic 'wire nuts', so soldering is not required. The component inside the module that usually fries is also replaceable, but if you are not familiar with board-level repairs, replacing the entire unit is preferable.