First of all, PS/2 is not a hot-pluggable interface like modern interfaces. The computer has to be shut down when you insert or remove a PS/2 plug into a PS/2 port on the computer, or the keyboard will not work. If you hot-plug and are really unlucky, something could get damaged.
Do turn off at the back of the power supply or yank the power cord just to be sure, as some BIOS:es might provide power on the PS/2 port while "off" anyway. (Mine does, and I can't find any option to turn that off...)
This does not apply if you use an active PS/2-to-USB adapter. (sometimes called "converter") - then it would be OK to hot-plug the USB end of it into your PC.
A passive PS/2-to-USB adapter won't work at all- those are for keyboards that are able to talk either USB and PS/2 over the same wires.
If the keyboard still does not work, do test it on another computer. Again, the computer has to be off when you plug it in or you would need to use a converter.
If it works on the other computer, it could be a driver issue. You should be able to upgrade the driver in Device Manager ... I think. (I don't use Windows 10 myself, but I think I read that somewhere...)
If it does not work, then there could be a faulty electrolytic capacitor that would need to be replaced. That is a common problem among old electronics, but not a common problem on the Dell AT101 specifically (that I know of ...).
I know that at least one revision of the Dell AT101 has two electrolytic capacitors on the circuit board.
