Help with iphone please

Hi everyone I'm having some issue with my iPhone 3GS. The housing is in pretty bad condition as the back is cracked and the power button doesn't work at all. And yesterday I got the the white screen of death and I couldn't fester it or restore it as Ive jail broken it and didn't want to lose the jailbreak. Anyway I suspect my connectors are broken either tab 1 or tab 3 though I found a a guy selling an Iphine 3GS for 10 pound which doesn't activate because it doesn't read the SIM card or something. What I wanted to know is if I pulled the mother board out of my 3GS and put it into his housing and used his LCD screen would I have any issues or would this work fine and would all my apps and photos and jailbreak still be intact?i have an iphone 5 though I use this as the 3GS as backup when my 5 dies so I would be grateful if someone could please help

Thanks for the help guys could you please just take a look at the tab one connector and confirm that it is indeed the cause of the white screen and if there's any fix for it