Can someone please help me with my iPhone 3GS?

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 permanently though I've had it for a few weeks so after I would press the top right hand corner down the phone would work perfectly fine until it locked again and then to unlock I would press the top corner agin and unlock and it would work fine.and I couldn't reset it or restore it as Ive jail broken it and didn't want to lose the jailbreak. Anyway I suspect my connectors are broken most probably connector 1 so I've added a pic if it below and wanted to know what my options are. If I put my motherboard into another 3GS would everything be exactly the same as before including all apps jailbreak and data? Also update I removed the LCD and left it on my windowsill and now it's completist stopped and I don't even see a white screen. Someone please help