You have a number of "if browser" logic wrapping some stuff for Chrome and Firefox. Are there things that are being done with those two browsers that may affect how the application renders in IE?
Also, something to check, albeit a bit of a fringe idea... are Chrome and Firefox somehow opening iexplore instances, like if they are emulating them or something? Check your task manager and make sure that there's not multiple iexplore instances out there. It's possible that the reason for the failures has to do with TC getting "confused" as to which instance of ie it's supposed to work with.