I believe there is a fuse in the back of the radio, I'm almost sure of it. Get the radio removal tools at Walmart and yank it out and look

As to the "general cooling system alarm light", grab a voltmeter and test for 12 volts on both sides of the 50 amp fuse in the little fuse box next to the battery, that feeds the Fan Control Module. Sounds like the Fan Module is not responding to the ECM. If the fuse is blown and a new fuse blows right away, replace the Fan Control module.