My 2003 Honda Accord radio makes a loud squealing noise and then goes out. The lights and buttons work fine.

Check the rear speakers to see if something in the trunk has disturbed the wiring and shorting against the speaker metal.

How did things work out?

The radio's internal ampifier may have failed. The only way to verify the fault would be to swap your radio into another car that doesn't have a problem and that radio into your car. See what happens...