These PS/2 to USB dongles are notoriously unreliable. I have come across quite a few over the years that similarly didn't work. All I can suggest is that you purchase a better quality one. I have a number that I use that support both mouse & keyboard and they work great. They are from HP, Airlink and (mostly) IOData.
Hope this helps,
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PS/2 peripherals are old now; the compatibility with the newer operating systems and hardware is difficult. I suggest you Scott’s recommendation.
As a workaround, verify in the BIOS if Legacy Boot and USB legacy are active.