Just a bit more detail here:
If your mat is outputting PS/2 signals, so if you want to use it without modification, you will need a PS/2 driver for your controller. There is no existing MIOS PS/2 driver, however if you’re a good coder, there are PIC PS/2 drivers freely available which could be made to work with MIOS. I assume the same goes for AVR, if you go the arduino route.
It’s not actually clear though - you’ve said PS/2 keyboard cable. Cimo said PS/2 dance mat uses HID protocol. I think Cimo has misused the acronym - PS2 (Sony PlayStation 2) and PS/2 (IBM Personal System/2) are not the same thing. The HID protocol Cimo refers to is most likely from a USB dance mat. So, the first thing to do, is give us a link to your dance mat so we have a clue wtf you’re talking about 
Now, it is entirely possible that you may be able to mod the mat so that you can connect directly to the pads, and not use PS/2 or HID. This one requires not programming but circuitry experience.
If you lack both hardware and circuitry experience, or if you lack time or inclination, the easiest way to get what you want, is what cimo suggested - let a PC do it.
So what we need to know, to give you the right advice, is:
What is this mat, exactly?
Do you have programming experience (ASM, C)?
Do you have electronic circuitry experience; and are you willing to modify the mat electronically?
Do you need a standalone box; and does it need to be very small, or would a SFF PC be small enough?
Do you have lots of time, or money?