This is what I understand from your description.
You developed a program for PIC 16F877A with 8MHz frequency but while testing you used 20MHz crystal. It was working fine when you switching on both devices simultaneously. Then you changed the frequency to 20MHz in the program and rebuild it. Now it is not working.
Firstly, you need to use same frequency in both program and hardware. If you use different frequencies you will experience lot of problems like this. It is very difficult to track the problem without project code. Basically it will be some hardcoded delay or baud rate problem.