Since the keyboard fails (albeit differently) with both the adapter and the "real" PS/2 port, it seems more and more likely that the board itself is to blame.
However, if you're in Linux (or another UNIX-like system, I assume - not very experienced with e.g. Mac OS) I think it would be worth looking into what the OS sees. With and without the adapter.
If you're in Windows, I don't know what to say. Linux is good at this kind of stuff
What happens in
when you plug the keyboard in? (Again, with adapter or straight to PS/2)
1) Try running dmesg, then plug the keyboard in, and run it again. Tell us if any new output has appeared.
2) When the keyboard is plugged in, can you locate a device file for it in /dev/input/ ? That would be very useful.
For instance, I am using a 90's Cherry G80-1800 via a PS/2-to-USB adapter right now, and I can access the raw input stream as HEX in two different ways. Either by finding the correct
/dev/input/eventX device file:

Here I am using the
xxd command (as the
root user!) to show hex output. Otherwise you get gibberish (the terminal trying to read binary output as characters ... ). Remember to press a few keys on the dodgy keyboard after running the command.
Often, you will also be able to locate the device by its ID, like so:

(Yes, my Perixx PS/2 adapter apparently identifies as "barcode reader". A sign of superior quality, no doubt.)
Let us know if any of this gives results (even negative ones!), both when using the adapter and when using straight PS/2.