It sounds like you have a couple of problems going on. Partial or no backlight plus Boot-Looping.
This would occur if the battery wasn’t disconnected or you have dislodged some tiny components around the connectors while you were changing the screen. Have a look under magnification and see if there are any tiny components around the connectors that are loose or missing.
Also check the screen flexes for tears and make sure the battery connector is properly in place. You should also try another screen and make sure the battery is good although the battery would not affect the backlight.
Next try and boot the phone with just the LCD connector attached and see if it boots to IOS but this will depend on the IOS version you are running, if the firmware is recent it should boot.
If you have ruled out parts or you have found some dislodged components you will need to have it fixed by a repair shop as it will require microsoldering.