I replaced the screen in one unit as well (completely destroying the old one in the progress like everyone does) and installed a new one. When I got the replacement screen it was delivered without the connecting cable to the motherboard (next to the connector for the digitizer and the battery) so I had to use the former one.
When I tried to power it up it would not show any signs of life so I connected an external monitor just to be sure and it worked like a charm. I found that the connection from the lcd to the motherboard was kind of wacky and wobbly so I used a small strip of duct tape under the metal strip which should do the job and it held perfectly.
By the way my unit would run easily without a battery connected!