You can do the repair yourself. The guide is available right here. Just familiarize yourself with it and do take your time. Follow the steps and be organized. The display assembly can be purchased from here When you talk about the backplate, and you should refer to the back of the iPod, that will be a bit trickier. Here is the teardown, it is not a guide, but will show you what you are up against if you want to replace it. If you are not sure if you want to do this by yourself, do a search with Google and see what the rate is for such a repair. Going rate seems to be around $90 for the repair. Hope this helps, good luck.
Replacement with the LCD and the digitizer fused together. — 50+ available at 64.95 each.