#1
So I have a grunge pedal and the + side on the 9v adapter broke up when I was replacing the battery. My question is, can I just buy another 9v adapter at radioshack, cut the old one off and use electrical tape to replace the part?
#2
You'll need to twist the wires together to form a splice, and they really should be soldered together before being covered with tape: the tape is only there to prevent electricity from flowing between the two wires, which now have a bare metal splice in them.

And you are lucky...I had that same problem, then my switch started acting up. before I knew it, the entire thing litereally fell into 15 pieces. Argh.