During the 1980s computer manufacturers tended to slavishly follow what IBM did making their products a de facto standard.
 
When IBM launched the Personal Computer (PC) the keyboard connected to the main part of the machine via a 5-pin DIN plug.  When the AT computer came out the keyboard had an improved layout and lock lights were added. Operating these needed a change in the protocol, ie the language the keyboard and computer use to talk to each other.  Some keyboards were made with a switch so they could use either protocol and some could automatically switch to the correct one.
 
A couple of years later the Enhanced keyboard layout was introduced which, apart from the addition of Windows keys in 1995, is the type that's still standard.
 
The next change was when IBM introduced the PS/2 range of computers.  On those the keyboard, and mouse, were connected via a 6-Pin mini-DIN plug; these often get called PS/2 connectors.  These remained standard until USB took over, and there are still (2018) some keyboards being made with PS/2 plugs and computers with PS/2 sockets.
 
All that's needed to use a 5-pin AT keyboard on a PS/2 equipped computer, or vice versa, is a simple adapter to change the plug.
 
There are also adapters to connect a PS/2 keyboard to a USB port but it's a bit of a mine-field.  Some are passive and do nothing beyond changing the shape of the plug.  These will only work on keyboards that are bilingual, ie that can use either the PS/2 or USB protocol, as the adapter doesn't translate PS/2 signals to USB.  These devices tend to look like this:--

What's needed is something that translates the protocol as well as allowing physical connection.  These adapters look like this:--​

The purple socket is for a keyboard and the green one for a PS/2 mouse.  These adapters USUALLY work but not always.
 
The best solution is a Soarer's Converter.  These were designed by somebody calling himself Soarer and details were published on keyboard enthusiasts' forums (yes, there really are such things).
 
Making one doesn't cost much more than buying an AT to PS/2 adapter plus a PS/2 to USB one and has more chance of working, though nothing is absolutely guaranteed.  They will also convert the old PC/XT protocol and even convert terminal keyboards that were never meant to work on stand-alone computers.  Besides that they can re-map keys and run macros.  There are people who make and sell them on e-Bay, at prices of varying degrees of obscenity.
 
The guide I used to make one is here:  https://deskthority.net/workshop-f7/how-to-use-a-pro-micro-as-a-cheap-controller-converter-like-soarer-s-t8448.html
 
I've amended this based on my more recent experience and that version is available as a PDF here.  It's handy to be able to print it to consult while actually doing the job.
 
I've also made a printable PDF version of the HID code list.
 
Some background on the converter and its creator is available here:  https://klikkyklik.wordpress.com/2015/08/28/soarer/