pic16f877 max232
I would first test the two separately.
First try using the hyperterminal with your LCD. Make sure the LCD can talk over RS-232. Just send ASCII characters to match the commands, etc. If meaningful things happen on the LCD, you will know it's working. At this point you can correct wiring problems, if any.
Next, using RC6, RC7 and a MAX232, connect to the PC, runnig hyperterminal. That way you check your PIC code. I would write a very simple code that echoes the character back to the PC. This will keep the code to a minimum, but it will help you detect wiring problems, as well as code problems, such as baud rate, enabling the USART, or fogetting to make the TX pin an output, etc.
Once you get that working, conect the LCD to your PIC board.
Now that you know that each module is functional, if the assembly still does not work you can look at your wiring, code, etc.
By the way, I don't think you need the MAX232 between the PIC and the LCD. All you need is a couple of gates, 7404. It seems to me this LCD does not use "true" RS-232 signals, just TTL level, which generally work with a PC.
However, only try using the gates once you have managed to make the two work together using the MAX232.