(O-Scope) Probe the "WP" pin of the RAM board while powering on and off and see what it's doing. The lower addresses of the RAM are normally write protected, which if I recall correctly is the purpose for the 7432. If "WP" is high then you can write to the lower addresses, and if it's low then you can't; normally it should be low. The interface ties "WP" high so the lower bytes can be written by the computer.
Also, the software SHOULD run on fast CPUs since it reads the hardware timer. The issue is whether or not the OS allows low-level hardware access to I/O ports. If you've got a classic LPT port that supports bidirectional transfers, and can boot DOS, give it a shot. To test without the RAM board, tie the DATA lines in a certain pattern, hex "A" perhaps, and see if you read all "A" and so on. If so, then you should be good to go with the RAM board.