If you replace just the LCD panel (and not the entire assembly), it will work fine. The reason there is difficulty with the display assembly as a whole is because the airport cables are different in the A1139 version (they combined Airport and Bluetooth into one card in this version, and it changed the connectors).
The keyboard for the A1139 version has a narrower connector than that of the A1107, so it is not interchangeable.
The hard drive cable has the same form factor, but a different part number. It's your call on whether you want to test it out or not. If it turns out that the hard drive cable isn't the problem, it looks like a logic board problem, so you may not be losing much by trying.
Good luck! Please keep us posted with the results.