After replacing battery screen doesn't work, It shows faint grid lines

What color are the lines? If they're grey/white it's a sign of a poor connection and/or ESD damage. You'll want to power off the device (hold the power + home button simultaneously) and then disconnect the battery, followed by the screen. Take a q-tip (dipped in Isopropyl Alcohol if possible) and clean the connectors on the board for the screen and on the part. Let dry completely (this goes faster with >91% purity alcohol) and then inspect for any debris in the port(s). Plug in the screen, then the battery, and then power on the device.

Lines should be gone but if they are not you may try letting the device sit, disassembled for about an hour or two for the static to discharge.