Yep, it's the adapter. They are not guaranteed to work on all USB keyboards, it depends on the keyboard's internal circuitry. In some cases it's the adapter itself that's cr*p.
If you really must use the PS/2 keyboard port, then you need to buy a native PS/2 keyboard (ie the wired plug is PS/2).
They are less easy to find these days but they are still out there at online vendors. Just use a search engine.