What you should do is buy these: iPod Touch Gen 4 Adhesive Strips so you can glue your screen assembly back on the rest of the iPod. Make sure all connections are OK and everything fits so you don't have to re-open it again.
Custom-cut adhesive strips for installing iPod Touch 4th Gen (Generation) display assembly. A must-have for any broken, cracked, or shattered screen replacement. Used to attach the display assembly to the rest of the iPod case. Made from high quality 3M d — 50+ available at 3.95 each.