i have the same problem.
1. plug it in with power chord
2. Apple logo pops up for 1 or 2 minutes
3. i start holding down button combinations, and the apple goes away, screen seems like it goes black. but at night you can see the display is fully lit.
4. holding "home and sleep" to get the red slider gets me a horizontal one pixel blue line, a quarter of the way down from the top of the screen.
if i plug in to MacBook pro...
5. same as step two above but
6. image capture launches and photo thumbnails appear from my camera roll, while apple logo remains on screen.
7. at that point i have about 30 seconds to copy photos to my desktop, then the phone restarts and image capture loses connection.
8. steps 6 and 7 repeat endlessly.
i have replaced the dock connector once, with another known functioning iPhone (we have two in the family).
i have also swapped batteries, but i'm having the same behavior...
i have a "new" dock connector coming in the mail, so i'll try that next.
in the meantime i'll swap logic boards to see if that is the issue.
unfortunately i've been out of hard disc space on MacBook pro so i have been unable to backup my iPhone. so it will be painful to RESTORE the phone.
[i have also swapped Headphone Jack Ribbon, and Power Sensor ribbon and removed a broken front screen from the phone i'm robbing parts from. i am using a highly organized system of ziplock bags to keep it all straight, so i don't think there were any errors.]