I have Java 1.7.0_03 on my system and I get this problem to. It has to deal with loading in old levels. If you roll back your version you can load in those maps fine, but when you try to load them in on the newest version you get this white screen.
I tried deleting my whole tekkit folder and then copy/pasting a save into the new one ... no luck. All it has out of the ordinary is Railcraft rails, wirelss redstone, logic gates from redpower2, Red Alloy Wire, Lamps, Rail detectors, alchemy chests, some slabs (or what ever those thiner blocks are from RP2) ... oh and some solar panels (high efficency or something like that), glass cable, energy links, MSFU, Wooden power pipe, power transport pipe.
The rest of the map if I recall right is normal and are items in the normal minecraft. I really hope I don't lose this world, I have put a lot of time into it, as well as other words (I am going to destroy the whole solar panel set up see if that fixes it ... seeing as I don't need it atm)
Update: removing that whol solar power set up ... didn't do it