The cheaper screens sometimes are more frail, but in the 98% of the cases the problem is the correct placement of the screen on the device. The screen of the ipod 4g, is glued and supported on the back aluminum case. If the case it is not straight due to a drop or other, or if the old glue of the old display it isn't removed completely when the new lcd was mounted, all seems to be fine, but when you press the screen on every day use the force is concentrated on this non straight or non cleaned points and from this points start the cracks. Remember that this glass, is non-scratchable because is hard, but at the same time, it is very rigid, and non elastic, so it have to has mounted on a very clear and plate surface.
Probably you have broke or bent the earpiece speaker contact. Check these contacts and be sure to have positioned correctly the top part of the logic board. When reinstalling thelogic board, be sure to clean it with a degreaser such as windex or isopropyl alcohol. The oils on your fingers have the potential to create bad contact. If you find your contact OK, check the erapiece with a TESTER and if it's broken, change it.
It seems have the battery drained out, if you can try charge it with another charger. Because if the charger has some problem, it isn't capable to charge the battery correctly.
Try to use the phone after restore, without loading the backup. In this mode, you are sure that any apps can make the microphone not working. Maybe you have some apps that interfere with the microphone.