If you have a steriliser, similar to that used for baby's bottles then half fill that with water and about 25ml of washing up liquid, put the sim on the top tier of the steriliser (not directly into the water) and switch the steriliser on. The heat and moisture from the steriliser will clean away the layer of dirt which is stopping the sim from picking up a 3G signal. The most important part is the rapid drying process though, as soon as the steriliser finishes it needs to be dried almost instantly, therefore whack this straight in the toaster (2 slice or 4 slice, doesn't make any difference), I'm almost certain that should solve your problem.
If it doesn't then maybe just stick some butter and jam on the sim and make a meal out of it