You could test the board by removing the PIC and VERY VERY carefully plug a jumper wire in across the PIC TX/RX pin sockets. That will give a loop back to the PC when something is sent.

And/or

Program the chip, put it ina breadboard then connect to the PC. If you have the hardware.
Use SEROUT2 with an inverted MODE then an inverter chip is not needed. Send "hello wold" like Bruce mentioned.

Jump pins 2 and 3 at the USB/serial converter and do a loop back test.

With out an "O" scope, write a code to send something in a loop, something long. with a second pause between sends. Connect a DVM to zero and serial pin #2 of the EasyPic and see it the is any activity from the on-board inverter chip. If the DVM fluctuates then the inverter chip is probably working.