There is no solution, the CPU cheats, in a 2 player match you can easily block throw,s by pressing back or down/back, this doesnt work against the CPU because he cheats.
Try to make early footsweeper,s to prevent getting throw.
Jump forward to the CPU, but dont use any move, just jump forward, then jump backward and if you timed it right the CPU just jump forward to you without any attack, than give him a uppercut, roundhouse whatever and repeat this pattern.

For beating the CPU in MK II (for 3.1 arcade, anyway)

If you are playing on the Player 1 side, this tactic works with Johnny Cage, Jax, Baraka, Shang Tsung, and the ninjas (possibly Kung Lao too, but I forget). The computer opponent will always walk straight towards you, so let him walk up to you until he gets just outside of throw distance (while waiting you can just stand there, step back, or crouch; I usually just crouch).

Now just jump back; the computer should just stand there for a second, then jump towards you. By the time you land, they will be in the air, ready for the attack or juggle of your choice.

And if you ever want a couple of quick hits, the computer seems to never block low, so you can usually get a few sweeps in before they throw you. But again, the CPU throwing priority is ridiculous, so be careful.

Oh and the keyboard won't be so bad once you get used to it... the MK controls actually lend themselves pretty well to keyboard use. For example, you can be crouching and still tap the left and right keys to do a special move.

Good luck!