I have all the DLC besides Dead Money and Gun Runners' Arsenal. I've beaten the game and started a new one so I can play the DLC. People say I should get a radio signal? I have nothing that tells me of my DLC in-game. How do I get them working? I also re-downloaded them all... nothing.

Sometimes they take a while to appear on the screen.
I usually get Honest Hearts warning after seeing Sunny Smiles and Old World Blues shortly after.

Check you haven't overlooked them by going to your Pip-Boy > Data > Radio
In the radio section you should see the

• http://fallout.wikia.com/wiki/Sierra_Madre_Broadcast (Dead Money if you get it)
  
• http://fallout.wikia.com/wiki/Happy_Trails_Expedition_Broadcast (Honest Hearts)
  
• http://fallout.wikia.com/wiki/Mysterious_Broadcast (Old World Blues)

If you have these stations go to Data > Quests and you should see the following;

• http://fallout.wikia.com/wiki/Sierra_Madre_Grand_Opening%21
  
• http://fallout.wikia.com/wiki/Happy_Trails_Expedition
  
• http://fallout.wikia.com/wiki/Midnight_Science_Fiction_Feature%21
  
• http://fallout.wikia.com/wiki/The_Reunion

Just follow these to their respected DLC - Hope these are present for you. If not start a new game and hopefully they appear (assuming you're not far into it)

- Its always good to have a save point right after leaving Doc Mitchells house, it saves doing all the designing again and listening to him talk when you can do it again before leaving Goodsprings.

I can't even start Midnight Science Fiction Feature! - oh I see the eye on the screen (between 12am-3am) but that's it.. didn't even know there was a satellite to activate until I read about it on Fallout Wiki.

I'm on the 360, playing the Ultimate Edition - even reinstalled the DLC - same effect. I'll try again later.. but does anyone have a clue?

Did you use the satellite...? (in the allotted time)
In all cases.... Always wait on the main screen until the dlc loaded screen has vanished (if you change accounts or are fast you actualy can start or load a game... DLC not loaded will not be in the game)

There is no satellite in my game.. all I see, is the projector light and the eye on the screen.. where the satellite should be (according to Fallout Wiki) I have a small crater.. I always wait on the main screen until the DLC is loaded but I get the same result.. oh well.. once I'm done with this character, I'll start again and see if the satellite is there.

Weird... have you tried deleting all DLC and the system cache.... (backup your saves before doing so)... This might be a last resort... otherwise yep... start anew..