No problem at all, rixwrites. It's fun to talk about one of my favorite subjects.
There would be no need to move it out of a junk orbit, and this would probably not even be possible. I believe satellites in a junk orbit always have their fuel tanks vented to prevent detonation when they are eventually impacted by space debris. A junk orbit is just one that is up and away from other satellites and high enough that the atmosphere won't cause enough drag to result in it re-entering any time soon.
I don't know much about specific radio technologies or radio bands, but I suspect a really sensible way to contact a satellite would be just the method you describe, but with an old satellite dish for an antenna. The dish needs to be pointed at the satellite, so you need to know it's approximate location in the sky, which would provide some good plot points and details for the characters to futz over. Using this kind of parabolic dish would make the signal appear much stronger to the satellite (and conversely weaker to anyone else if your characters are trying to hide their signal at all).
If it's not in a geostationary orbit, they will have to follow the satellite across the sky, which might provide good futzing for them, or it might interfere with your plot. If it does, an alternative would be for the comm sat to actually be a satellite TV broadcaster. Regular old satellite TV equipment would pick up the signal, the location could be looked up in old manuals, and the satellite will already be in a geostationary orbit (and thus not need a graveyard orbit).
Solar panels slowly produce less and less power due to exposure to the intense radiation in orbit. I think it would be safe to say that this satellite still produces enough power to weakly power one of its transmitters, or maybe to trickle charge its battery and thus produce a few minutes of communication time a day. Whichever is better for your plot. It would have been retired because it didn't operate reliably, or it couldn't generate enough power to run all the transmitters or maybe it was just too old and slow and a much better satellite (that didn't survive as long) was launched to replace it.
All civilian satellites are definitely solar powered. The only nuclear satellites are government experiments, or government deep space probes. (Believe it or not the Soviets actually orbited a complete nuclear reactor and then accidentally smeared it across Canada. Canada sent them a bill for the clean up.)
An alternative if you want a low Earth orbit would be the Iridium network. There are tons of those things up there, and there are a lot of publicly available details, so you could include a lot of that for delicious texture. They can be communicated with via satellite phone hardware.
http://en.wikipedia.org/wiki/Iridium_(satellite)#Satellites
No satellite is ever told "stop listening to signals from the Earth", so they are always listening, even after they've been officially deactivated. Deactivation primarily means boosting them up or down into a less used orbit (to minimize risk of collision), venting out the fuel, and turning off the transmitters (to free up bandwidth). There is really no reason to turn anything else off.
I should also point out that I don't have any special knowledge in this field - I'm not in the industry or anything. I just read a lot about space.