check the antenna that is connected to the charging dock, also use a degreaser such as windex. Put light windex on a microfiber cloth make it very damp and gently rub it along the charging port front side where the metal prongs are and also rub it along the inside of the metal frame along the right and left edges. I am experiencing a similar issue after replacing my lcd, i am not having issues with service or reception but i can not connect to wif. Any idea where the wifi antenna may be located?
It is possible to remove the lcd from the digitizer but its a very difficult and tedious task. The best way to do this is to use a heat gun, but you have to be very careful that you do not "cook" the lcd because you can potentially damage it. You have to carefully heat the glass and slowly and very carefully pry the lcd from the glass, i do not recommend doing this because the end result will more than likely be that you end up damaging the lcd so it's really not worth putting that much effort and time into doing this.
I have seen this issue many times as i've repaired plenty of iphone 3g's. The main cause of this is from the impact of the fall related directly to the mother board. Generally if you replace the LCD with a fully functional and tested LCD and you still get a white or flickering screen it means that the FPC Connector on the mother board has been damaged from the impact of the fall. The FPC connector is the part where the LCD is plugged into the mother board. The FPC connector can be replaced but it is not an easy task, it requires patience and precision and working knowledge of soldering.