Hi mate, Sounds like you have purchased a poor quality camera. When purchasing ANY replacement parts, only buy from reputable suppliers and ensure the goods state they are original iphone parts. A lot of the parts floating round the ether are very low quality fakes produced in Asia for peanuts. You would be safe with this part from iFixit. Hope I helped.
The 6R8 coil is definitely worth investigating as this is usually the most commom cause of backlight failure after water damage. Also as Hector suggested this could be a corrosion issue. Which will need a good old touch up / reflow and a clean with 99% alcohol to remove any unwanted residue. On the positive side, neither is a difficult problem to fix :)
I would also go back and check over your other replacement parts and ensure everything is hooked up right. Especially check the dock connections. You have probably assembled correctly but maybe havent pushed one of the cables right home.
It depends how confident you are with the repair. I have never bought an assembly and think the components are an easy enough repair. On ebay you can get a Digitizer and LCD for about £15 / $22 The parts have always worked for me and takes about 10-15 minutes to fit. Its your call as OT's suggestion would be slightly easier, and slightly quicker but cost a lot more. As far as the quality if you look through the listings on ebay many sellers offer 12 month warranties on their parts too!
Just open it up and check all connections. Especially the battery and the logic board connections. The way the screen gets that white haze definitely shows a problem with the display. Is the phone definitely turning off, or just the screen losing picture? Have you tried calling it after its crashed? May just be a faulty display. If it is definitely turning off then I would certainly say it needs a new battery. Changing the sim card wouldnt change anything.
What makes you think the fault is software related? Did you notice the issue after an update / jailbreak attempt? Firstly, try resetting / restoring to see if that works. If not, then I would say disassemble and check your connections, especially cable 2 at the top end of the phone. Did you definitely buy the right version of touch and fully secured it? Sounds stupid but you wouldnt believe how many I repair with the wrong touchscreens on or the cable only half way home. Hope I helped.
Old Turkey is spot on here. First call would be the 6r8 coil. If still dim then I would replace the screen but more than likely it will be the 6r8. Dont replace the logic board until all esle has failed. Its expensive and usually un-necessary!
Hi mate, Sounds like you have buggered the charger port at the base of the phone. Firstly reboot the phone, just to make sure this isnt the problem. Try plugging into iTunes, if this also has no effect then you have clearly broken the port / connector. However if it does charge / register, then you may have not properly connected the battery, or your plug socket is faulty. Hope this helps!
So holding the home & power buttons the white screen stays? I would try booting out of DFU. Hold home & power for 10 secs, then release HOME and continue holding power. Then try hooking up and restoring iOS 5 and start again. Make sure you havent got a fake red snow too!