Why won't my screen click back in place?

Everytime I work on an iPod Touch 5/6, I always swear it will be the last one ;>). They can be frustratingly difficult to work with and the screens are so brittle and fragile that they will break under the slightest stress.

It’s very important to get the right screws in the right place and insure they are properly seated (but not over-torqued). Because you replaced the battery, you had to take all the guts out and its possible that something isn’t seating properly and causing obstruction. Take a break, regroup and try it again, this time by dis-assembling everything and looking for proper fit.