Wow, a classic
L2 is a power lead. Replace the burnt wire. Get 2 quarter inch female hi-temp resistant terminals and some 14 gauge hi-temp wire. That should do it, unless the switch itself is bad.
I'm not sure if RadioShack carries hi-temp terminals and wire. We carry both the terminals and wire but I don't remember part numbers off hand.
Contact our parts department on Wednesday and they'll find it for you.
Hope this helps.