Is a 1st Generation screen compatable?

I bought a 1st Generation iPod Touch a while ago, with a cracked screen. The screens break on those all the time so I always just buy them like that because they're cheaper, but still work fine.

So anyway, my dad went online and found a screen replacement, so he bought it for me. But, before it actually arrived, the iPod stopped working. It just went black and won't turn back on. Even when I plug it in, it just isn't awknowledged. The Home button was starting to get unresponsive for a little while before this too.

So anyway, now that my g1 is dead, I wanted to by a Third or Fourth Generation touch. I found a few, but they all have cracked screens. Because like usual, that's the only way I can afford it.

But I already have a good 1st Generation screen replacement, and no iPod to use it on. I was just wondering if the G1 screen would work on any other generations. It seems like it should, because the parts are practically identical, and it's just the glass screen, not the touch screen or anything.

So, ah, yeah. That's my question. Would the 1st generation screen be compatable with any other generation of iPod touch?