Will I benefit from a new lcd?

So basically, my brother gave me his old iPhone 3gs. He had dropped it before so the casing was cracked, the mute button wasn't working and the lock switch had fallen out. I decided to order new casing and whatnot to fix it but everything else about the phone was working.

Now I switched it to a new case and it was functional except for the mute switch. I had taken it apart again and finally gotten the mute switch to work. But minutes later when my screen had shut off it would give me a white screen. A hard reset of the home button and lock switch would fix it until the lcd shut off and I would be welcome with the same old thing.

Now what I'm wondering is if getting a new lcd will fix this phone or not. I can still use voice control,music works, the mute switch works, calling works but the lcd is non functional. So do you guys think it's the lcd or the logic board? I'll attatch two pictures of the three connections (the best my camera will allow) to see if it looks like anything's wrong. If guys don't think it's possible I'll just have to let my phone retire. Thanks

http://i42.tinypic.com/6jq44w.jpg

http://i39.tinypic.com/2i8f6uo.jpg