I have the TH-F6A but I don't have the computer connection. However, I learned my lessons from connecting GPS' to PC's.
Did you set Menu Option 9 on the menu to PC? It must be set to PC in order to work. Also, the COM port that you are using can only be set to 9600 baud. You can adjust this in Windows (assuming that you are using windows) by going into Control Panel->System->Hardware->Device Manager. Click on the (+) next to the Ports label and select the port that you are using. Right-Click on the port and select the tab called Port Settings. Set this to 9600. You may need to reboot for this to take effect depending on the version of windows that you are running.
This should work for you. If not drop me a line at KD5OEQ@arrl.net
It could be that you have your serial ports turned off in your BIOS. Some machines, especially older ones disabled these ports to use the IRQ for something else.