How to fix Blank Screen but the Phone is Working?

I Have Iphone 3GS 16gb, I got it off ebay for £30 the Screen was smashed and was unknow if working. after getting the phone I checked for water damage and the was no sign, I fix the screen and had the phone working for 5 days then backlight started going off and on. I then check the for damage on motherboard but the was no sign of damage after putting the phone back together the phone was fine for a day but then the screen stop working and was blank but the phone is still working and works in itunes, I have put a new LCD and it still not working. I have try resettinng and everything but coz I have downgrade 4.1 and I now cant update only re jailbreak to 4.1. Am just about ready give up! anyone got any ideas?