A character that goes Berserk...
cannot use any skills, Edges, or maneuvers that require concentration, including Shooting and Taunt, but not Intimidation
How does this affect the use of Powers?
It seems clear that Spellcasting, Psionics, and the use of Weird Science gadgets requires concentration, and is thus impossible for Berserk characters. Superpowers are usually considered to be innate (Superman does not think of flying or being strong... it is just the way he is), so it seems they should be allowed to Berserk characters. Faith seem to be in the middle: if acts of faith are thought as canalization of divine energy driven by the character, they are like spells (and thus forbidden); if they are gifts from a deity that the character takes for granted, they are like superpowers (and are thus allowed). It may depend on the particular setting.
I have tried to find any official ruling of this, but I have been unsuccessful. I wonder if anyone has thought about this problem before, and what they did for their game.