I rigged the megaton bomb to explode, as Mr. Burke requested. But now when I go to Tenpenny Towers to meet him again, I can't talk to him. When I try, I just hear the 'click' sound that plays when you target a non-activating object. Frustruated, I decided to detonate the bomb without talking to him...but there was no explosion. The sound and scripted events happened, but no pretty explosion. Could this have anything to do with the fact that I can't find Tenpenny anywhere?

Well, You need Tenpenny and Burke together since when the explosion happens, Tenpenny says to Burke to give you a reward. I hope you have a previous save on hand x_x

I don't know why Tenpenny is gone though. The only thing I've done in the Tower is let the ghouls live there.

Tenpenny "leaves" the tower when the ghouls move in. As for the explosion, if you have mods affecting Megaton you won't see the explosion. I never get to see it either

I just havent got the heart to blow up Megaton, so as soon as I see Burke and had is little chat I just kill him there and then I go and pay Tenpenny a visit then drop his corpse of the balcony.