There's a small chance that even in the same model monitor they could have different guts. You may want to ask the seller to take a quick pic of the insides but chances are he hasn't/wouldn't open it. But as I said, a SMALL chance.
Beyond that, it would be much easier and less risky to transfer the main electronic boards from your LCD to the EBay one than to try to transfer the screen to yours. Make a note to transfer every disconnectable board from your old LCD to the EBay one. Even the power supply. Even though it lights up, the problem could be one output of a multiple output PSU is bad and not powering the electronics. No way to tell unless you had schematics and test guides showing expected voltages, etc.
THIS IS A BIG, DELICATE JOB. If you're a novice hardware hacker, consider this carefully.
If you've never dug into a piece of high-tech electronics, don't try to do this on your own. At the very least, get someone who's experienced to look over your shoulder. Just getting the case apart without breaking the case and the delicate inner bits can be a challenge if you haven't done a few and know all the tricks.
One big tip: Get a Sharpie indellible marker and mark every connector A, B, C, ... as you take it off the board or pull them apart. Mark the board side and the connector side with the same letter. Put a piece of tape with a piece of marked paper around a connector's wire if there's no way to mark it. You'll be glad later. Most devices try to use unique connectors but some don't. I've blown out a lot of equipment in my past just because I forgot to label connectors and I was "sure" of how they went back together.
Make sure you mark the same cable on each unit with the same label!
Go slowly, ask for advice, and leave the hammers in the toolbox.
- The Inspector