I can't seem to pull this off on keyboard can someone help?

The Slide move is Back, Low Punch +Block + Lowkick. You have to do them all at the same time.

You don't need the back key. The key combination in the PC DOS versions is normally just BL + LP + LK. It works best if you press BL first, and the LP and LK together immediately afterwards.

So has anyone figured out how to do his slide? None of the suggested above works.

What about with a Logitech controller? Is this playable with one?

On the DOS versions you will only need to hold the block button with MK 1, I asked John Turk personally, I said hey Mr. Turk one of the twelve people who use the GOG forums has a question, how do you do your slide sir, and he replied with this. MK 1 as player 1 press Z + N + M + J. MK 2 as player 1 press Left Arrow + Numpad 3 + Numpad 1. MK 3 as player 1 press Left Arrow + Numpad 1 + Numpad 3.