I have similar experience, just two days ago I replaced my 3gs LCD. Everything seems right, I checked and rechecked connectors 1, 2, and 3 to make sure they're all placed correctly. When I turned it on... the display on but showed "white backlight". When I charge my phone, I hear click sound, so I am sure the problem in on LCD.
Here are the steps I did to solve my problem: 1. connect 3gs to itunes (on my laptop), all apps were displayed virtually on my itune; 2. reset the system software to factory setting (thankfully itune ask backup all data first); 3. folow itunes instruction until the system restart on you computer, if you can see any instruction on your iphone display, then everything will be fine; 4. restore all data and iphone system to newest version.
This is what I think the possible problem, either when you replace your digitizer, your iphone wasn't turn off or the iphone system software does not recognize new part replacement (digitizer or LCD) so it requires system resetting with iTunes.
Hope this info could be helpful.