Had the same issue. You need to go to location that saves the mod files (C:Users%UserAppDataRoaming.technic in Windows). Save any worlds you don't want to lose and then delete the tekkitmain folder. Everything worked for me after that.
There was once a 'clear cache' option that did something similar, but I can't find it on the new launcher. That would be a better way if someone knows where it is.