Do you still see dim lighting when it turns off? Have you tried another hdmi cable or maybe another type like vga? Do you smell burning? Extra heat maybe? If not check your solder job. Maybe it shorting out. Heck, even try another power cable.. Find Schematics ans test voltage..maybe the backlight or receiving to high of voltage.. maybe even got the wrong or cheap backlight filters? Just helping with troubleshooting.

I would take the phone apart and again inspect everything on the board, then (sucks i know) but remove the shields and inspect the board. You can leave that board drying for days and days in a warm closet in a ziplock bag with rice and all i think of is Humidity in that bag. Remove the shields and then dip the board in 99% isopropyl alcohol and take a toothbrush to it(that is if you do not have a ultrasonic cleaner). Once you remove all the shields and have done that, let it sit and dry then reassemble. If you cannot take the shields off then just dump the board in the alcohol and shake a bit(its still something). Also for components (if you notice oxidation) dip the connector in alcohol and scrub with toothbrush..I dont know your experience level or what equipment you have so i tried to list both sides of the spectrum...try it and let me know how it goes.

Connect phone to computer with iTunes open. Then on the iPhone hold power and home for 10 seconds, then release power button but hold home button another 5 seconds. iTunes will see the phone in dfu mode and try and restore it. Here's where it sucks..iTunes will try and update the phone and one of two things will happen, either iTunes will update the phone or it will get stuck on waiting for iPhone then eventually you get error 9. If that happens then something is bad on the board..

Uh oh. I had this happen before and turned out to be a blown capacitor on board. I had dismantle the back panel and searched the entire board. When I found the capacitor i knew it may be the culprit because all capacitor are flat on the end and this one was rounded. Took a soldering iron to remove as much solder as I could from the capacitor spot and then I took a heat gun to it to pull the capacitor. Be sure to use that yellow heat disapating tape around the capacitor so you don't over heat nearby capacitors. Find the same capacitor on eBay and that was it for me.

I had this problem too and I figured this out and fixed my wifi signal...take a look at the speaker of the iPhone. You will noticed a bunch of little hooks located on the north side of the speaker. Make sure that those little hooks go under the frame(that's the metal under where the battery is seated, then screw the speaker down and make sure no hooks lift. Also take a look at the wifi antenna, there is a piece where an abnormally long screw goes, make sure there is a metal clip there! If you don't see that piece than you lost it while you we're fixing the iPhone. That metal piece is required for good signal.