I bought an RS232 to 0/5 Volt module in order to overcome the problem. I connected the Tx--->Rx in order to check if it sends the correct data.
It does not sends the correct data. I changed the baudrate to 9600 and then it sends the correct data.
As far as my major problem is concerned (that the my post belongs), could the 38400 bps be a problem for the strange numbers I get on the terminal PC, when I connect the PIC????
The 16F877A which I have is dead. I have ordered two new 16F877A's. I will get it in another 4 days. Wait till then. Once I get them I will test it on EasyPICv7 and report back. I also have to get 16 MHz crystal.