The red light, is it on a small box maybe about the size of a pack of cigarettes. If so that is the fix for the refrigerator to protect it from starting on fire. Primarily when running on AC power. when the heating units shout out.
The thing is it can be so sensitive to current changes that it can false set.
This turns off the 12 volts and disables the 120 volt AC heaters. That is why you lost all the LED display and operation.
One can power down the refrigerator and run a small, but strong magnet along the front surface and also along the edges to try and rest the read relay that acts to power down the units.
There is a way to remove the safety circuit, one was removed from a unit at the Rally in Gillette and reverted back to its original configuration. I did not see just what they did to get it running or the connections that where changed though.
As a note regarding keeping things cold. One trick is to place the ice in a separate container that fit will into a cooler, Add some rock salt to the mix. This lowers the temperature in the container. You will use a little more ice, but things can be keep cooler.
Think of an old fashion ice cream maker.