Your situation fits a classic Electrical Over Stress signature, which seems to be occurring often on these Raduinos.
I don't know how the were handled up to and including the recipient. Mine wasn't shipped in ESD protective packaging. :(
First thing you should do is read/dump out of the stored settings/data in the EEPROM.
You most likely will want the calibration data to lessen future headache.
One way to do this is to load IAN's firmware and use the BITX manager software to read the data.
Alternately, you can write a sketch to read EEPROM and print to a console / save the output.
It's not too hard to remove the Arduino NANO and replace with another one. Much cheaper than buying another Raduino.
Nanos from China are in the $3 USD range. Many threads on BITX20 on 'how-to' replace the Nano.
If you are wanting to move forward right now, you can comment out the CW read pin section in the sketch (no CW) or use the unused A7 pin for the keyer. (I _think_ that's the purple wire on the 'digital' pigtail)
Many good choices to 'upgrade' the micro-controller, but I would get my stock configuration BITX working first.
I know this reply is vague, if you need / would like future coaching, there are many here to help.
I will do my best to answer any questions.