I decided to send an email to the manufacturer of the RS232 board. The email was what I posted regarding how I've set this up with the pins on the Uno and how they were connected to the RS232 board.
This is his reply, and I'm hoping someone here can help explain this to me, as I thought this would work with the Uno:
"You need to connect the rs232adapter to the PC, not the arduino board. If I understood correctly, you connected the PC to the arduino board, then softserial to the rs232 adapter and nothing on the DB9 end, correct? Your example will not work."
I believe that what he is saying is correct (as you know from before, my understanding of the terminology (such as "softserial") isn't the greatest. I know that there is nothing on the DB9 end, and of course the PC is connected to the Arduino (through COM3) using USB, and the Arduino is connected to the RS232 using the software (not hardware) rx and tx pins.
is it surprising that the example program that was uploaded to the Uno won't work for testing the communication?