I know BAB can't be used with powers. Does this include special abilities like Transporter Move-and-Attack or a Sentinel's Multiattack or Capture? Thanks!

All of the above are powers. You can't use things that would take place after the attack is over such as Capt America or Citizen V' special white powers if you use Back Alley Brawl.

I'm sorry, Dirtybird is incorrect. Back Alley Brawl puts powers, feats and team abilities off limits for use if you want the bonus. The abilities mentioned in the first post are just that, abilities, and therefore are not precluded.

Actually, the things he listed are NOT powers. They are abilities. As such, they can be used with getting the benefit of BAB.

Wow, that's cool! That helps me out a lot, actually! Thanks for the help, guys!