I have exactly this symptom and situation.
I replaced the digitizer and when I attempt to power it up, the screen lights dimly for a second then it vibrates every 10 or 15 seconds. This continues until the battery is removed.
I verified all the connectors and even tried another digitizer since I bought two of them.
But no go.
I'll report back if I can figure out what's wrong or what to do.
Does anybody have any suggestions?