Lets see what I have there in the Code...
CodeGT_OreDictUnificator.registerOre("10kEUStore", new ItemStack(GT_ModHandler.getIC2Item("reBattery", 1).getItem(), 1, -1));
...You haven't installed IC² properly. That is the first Location, where a Nullpointer from an IC²-API call doesnt get caught (everything before that is hard enough to resist Nullpointers from the IC²-Item-API), and I highly doubt, that the reBattery has been renamed or removed from IC².
Tried removing IC from my mods folder and re-downloading the beta 1.112, didn't work. Checking if, after removing GT, if the RE-Battery's still there.
EDIT: Whoa. Got a crash from Advanced Solars. And then, removing everything IC2-related other than IC2 got me a Forestry crash, presumably because of the Electric Engines. Curiouser and curiouser. Perhaps there's a newer "open beta" thread than the one Mistaqur's Bitbucket page links to? I'm using 1.112.170-lf, tried re-installing after I saw your reply.
The only thing I can think of is some IC2 add-on having an item ID conflict with IC's RE-Battery. Which isn't right, since I got a crash from Mistaqur's NEI plugins and IC2 and, afterwards, removed only the plugins and the battery was there, all right. Trying ID Resolver just to be sure.
EDIT again: Not an ID conflict, ID Resolver didn't report any before I got the crash. I'll start complaining on the "open beta" thread.