DuPont connectors equates to logic level signals. There may even be a 3.3 v <>5v link selector on the adapter.
Whereas DB9 equates to "RS232" level signals. Generally, at least the capability to accept those voltage levels, even if not necessarily producing them.
My first step tends to be to connect tx to rx and see if characters typed in a terminal/emulator get echoed.
An RS232 breakout box is pretty much a given necessity, when it comes to sorting out what's happening on all those pins and sorting out what to connect to what.