I have defeated the big crab-like Queen in the Castle. Preston and another Minuteman are standing in a wall breach and continue to speak that we need to fix the radio. I have wired everything up and the 10 power requirement is green. But the settler icon is red. The game just doesn't seem to allow me to assign any of the NPCs to the station.

I have started a settlement there and reqruited some settlers with my own radio transmitter. I have a plenty of water supply from the pump outside the castle, food, beds, etc. Only the damn transmiter prevents me from continuing my cooperation with the Minuteman.

I struggled with this one too for a little while. I had to attach 2 medium generators in series to the power connection on the hut before the tower took off, then some dude just sat in the chair a little while later to be the DJ and hasn't moved since. No assignment necessary (in my case).

I read about that problem in a different post. It seems like for whatever reason your random minuteman was not assigned to work the tower, and it looks like he is essential for it to work, since he does nothing else but sit there... :/