Check fuse 4 in the fusebox. That provides 'radio' power and lighter power (and the signal to the antenna). Remove it, clean it, reinstall it or swap it with a known good 8 A fuse.

Fuse 1 provides 'lightbulb' power.

Your symptoms are consistent with a bad fuse 4 or a disconnected power line.

Remove the ashtray, remove the two screws holding the tray in, go a bit deeper and look for the other connectors. Look at the attachments in post 10 in the first link. That's what you're looking for behind the ashtray.

<<CAUTION>> if the ashtray was disconnected, it was probably for a reason. Maybe a stuck cig lighter, maybe a short elsewhere. Maybe the PO (since there's no mention of how long you've owned it) had a different radio and didn't fully restore the connections, or maybe he modifed the wiring for an iPod or something. Be aware of overheating and/or burning smells. It may not be a problem, just something to be aware of.