iPod Touch 2G broken screen A friend broke her iPod Touch 2G. Additionally, some water got inside. Now the iPod sometimes doesn't start at all, or just freezes and doesn't react to finger touches.

There isn't any background light anymore (or at least, I don't remember there was or if there wasn't)

Because there's no explicit digitizer included in some offers, my question is, is it even possible to seperate the front glass and the digitizer? 

My position is that, if there's a cable attached to it, there must be a digitizer too but the owner of the device disagrees with my opinion, so I am asking here for a definitive answer.
I haven't seen them sold separately. I imagine it is possible, but good luck finding one or the other by itself.

You can get the "front panel" assembly here ($70), which includes: touchscreen glass, integrated digitizer, metal frame and home button. Install directions here.

The front glass and digitizer should fix the touchscreen problems, but you probably will need a new display to fix the backlight (I haven't seen the light sold separate from the display). You can get that here ($60), with install directions here.

Hope this helps.