Mr. Gerald. I would suggest that you write a small program on the microcontroller that loops over and over again sending the same character to the serial port. When you write something to the serial port, it takes some time before that byte is transmitted. Then u get the Transmit Interrupt. Try configuring your microcontroller to operate at 9600 baud rate. Use an 11.0592 MHz crystal. If you have access to a logic analyser or some tool with which you can see the bits that you are transmitting, it would be more helpful in zeroing in on the error. (PC should not be connected to the port pin)

Write a similar program on the PC (with out microcontroller connected to the PC). Monitor its transmit pin as well. Once you see the start/stop bits and the data bits that you are sending on the logic analyser, go one step ahead. The microcontroller should now send the character and then wait for the reception of the same character. The PC should transmit what it receives. U can use an LED to indicate if communication is good.

Let me know if I can help you in anyway.

Regards
Aman