When you replace an iPhone 4 screen you are required to take out the antenna bridge assembly (the part that gives signal to your phone).
Below is an image of the antenna bridge assembly by itself. Circled in red are the four metal feet that help with overall WiFi and phone reception, if any of these are broken or missing (which is easy to do as they are very fragile) then it will impact on the overall reception.
Below is an image of the antenna bridge assembly inside the actual chassis of the iPhone. You can see why the feet are so important as they connect to the main chassis and use it as the antenna.
Below are two images of one of the two screws that secure the assembly into the chassis. This screw placement is more important as the other as it also connects with the chassis as the antenna.
Below is an image of the actual antenna cable connected to the logic board. This is the MAIN connection and if this is not securely connected then you will get very minimal GSM reception.
If all of these parts of the antenna bridge assembly are connected properly and not damaged, then you will most likely need to replace the antenna bridge. HOWEVER before you do that you should carry out a full firmware restore/hard reset (disconnecting the battery for several seconds). My guess is that you have been unaware of these small parts and have accidentally damaged them through repair process (i did exactly the same thing when i first started fixing i4's)
See how that goes and we will go from there :)