sure you can clean it - and if you're lucky it would work again
first of all, get some isopropyl alcohol (>90%) or some electronics cleaner and a soft paintbrush. you will also need soe tools to open the iPhone. use the logic board guide to disassemble the phone, the needed tools are listed in the guide.
open the phone and clean every odd loking spot (white/greenish residue) with the ipa and the paintbrush, be careful, the parts are tiny. take special care around the home button, let it dry and then reassemble it - good luck