The radio cannot have the volume or station changed,or be turned off. The LED light is always on.
The radio has internal problems though I would think the power to it should cut off with the ignition switch. If you want to keep the factory radio you may be best off looking for a replacement from a salvage yard or check on Ebay for a replacement.
Since you didn’t share information such as the car’s odometer mileage or model year with us, it is not possible for us to know whether the car might still be under the bumper-to-bumper warranty, but the warranty is one factor to consider–if appropriate.
is it an aftermarket or factory radio?
Is it just the LED that’s staying on? If so, it’s probably a theft deterrent setup
Sounds like Tom and Ray put that stereo in for you, check to see if it’s plugged into the power supplies correctly, if it’s in wrong, BINGO! problem solved, and that’s going to be a little work on your end, but it’s otherwise free.