Is it possible to connect the display cable directly to a DVI?

Sorry, No can't really do that. It's a long story.

I should not really say no because technically it can be done, but it would be crazy hard to do on your own, something for an electrical engineer or someone really into modding or both.

They are people that are into doing this kind of thing...........people that run dumb terminals and need a special very small screen for modding etc.

You need a schematic of the lcd to figure out a connection to make your own, most LCD screens in laptops are made by a large company like LG. however the mounts on the logic board are proprietary this means each brand has there own connections to the motherboard and now most are a ribbon cable consisting of 20 + wires, something like that.

You would need a compatible controller that would work with it or i guess some kind of DVI receiver too in your case and a way to power it all that would cost $ and these are all things the laptop does for you.

then figuring out all the cabling (the cables are usually short, and hidden within the hinge assembly ............so getting the screen to a point where it looks like it does now in it's frame would also be hard.....

so they are some logistical issues to sort out too.

They are places that do this, but again they cost $

This is one of the places:

http://store.earthlcd.com/LCD-Kits

You could contact them and tell them what you want to do, i wouldn't be surprised if it ended up being expensive. Most places that make this kind of hardware do it for large companies, they are other places that do this too.

usually a solution once found will be some kind of low graphics anyway. (for business applications)

You could just sell your broken mac, they go for good $ on ebay......and buy a 1080p 22inch inch LCD...... (keeping your hard drive if you don't secure wipe the data off it). I have a 22 mounted on the wall, swings over the desk.

Why do you want to reuse the display? (special flush mount some place or?)