Ross,
I'm a recovering audiophile. I unknowingly joined Audiophilics Anonymous when I took the two steps in their program: marriage and parenthood.
All kidding aside, you're in an all-too-familiar quandry faced by millions of users of stereo products (audiophiles and non-audiophiles alike) who have purchased integrated "receivers" instead of individual components (tuner, pre-amp, amplifier, etc.). The diagnostic and repair prices you've quoted are directly in line with what I've seen. So are the prices of new receivers.
I've never owned anything from Denon, but they used to have a very high reputation. If you really want to know what's recommended by audiophiles, buy a few audiophile magazines and see what they have to say. I used to know all the titles, but I haven't walked into a newstand in years...
If your Yamaha isn't all that old, and the rest of the unit is working correctly, AND you don't need (or already have) all of the new bells and whistles available today (video source switching, surround sound decoding, etc.), then I have a few suggestions:
1) Get a separate radio tuner (AM/FM or FM only; if such a thing still exists on the market today), and connect it as an "auxilliary input" to your receiver.
2) If you have cable or satellite TV service, check to see if your provider offers music-only channels (for an upcharge, I'm sure), and route the audio output from your cable/sattelite box to your receiver.
3) Check out sattelite radio. I don't know much about it, other than the fact that it exists, but it might offer something attractive to you.
4) If none of the above works, and you've got a broadband internet connection, you may be able to find a web site for your favorite FM station, "stream" their broadcast to your PC, and play it through the PC's speakers, or, depeding on your sound card and it's proximity to your stereo, through your receiver.
By the way, I'm familiar with the "my stereo is broken and I can't afford to fix it right now" problem; my 20+ year-old Pioneer speakers are distorting so badly that I disconnected them at this time last year, and I still haven't repaired or replaced them.