A lot of things could have gone wrong here. The good news is that iTunes still sees your device. That means the failure is related to the backlight or display circuitry. Did you have the battery disconnected whenever you removed or installed the LCD/Backlight connectors?
Otherwise, the biggest challenge for users when they try to fix their devices are avoiding Pry Damage, Broken FPC Connectors and Long Screw Damage.
Pry Damage - If you are not careful when removing the flex connectors (such as the battery connector), you can easily pry away tiny surface-mount (electronic) components which will cause all sorts of problems. This also happens when removing the battery improperly.
Broken FPC - If you insert the connections incorrectly and apply too much pressure, you can damage the very delicate FPC connectors. You really need to look at them under moderate magnification (10X) with a loupe or microscope to see if they are damaged.
Long Screw Damage - As you suggest, the screws holding the various brackets have different lengths. Sometimes, only a tenth of a millimeter but that is enough to dig into the logic board and cause damage.
If you don't have the tools necessary, you should consult with a qualified repair shop that does micro soldering for a proper diagnostic.