Why parts should I replace?

I have an iPod touch (1stgen) which has a vertical crack in the screen. You can't feel the crack from the outside but it's definitely visible. The iPod will work, charge, etc. but only if I squeeze/ slightly bend the device together vertically. When you do this, there are not visible blotches like you would normally see if the lcd is broken. Only the vertical crack is shown. I know that I need to replace the screen but I wonder if the digitizer and lcd need to be replaced as well. Any thoughts? TIA : )