Quoted from SteelTigers:

Sounds like a ground issue. Does your sound and speech board have all the screws attached to hold these boards to the sound board mount on the back box? Have you checked the header pins on the pcb and wires on the connector at 10J3 on the sound board? Look for cracked solder joints on each pin on the 10J3 header, reflow solder if necessary. Then check the IJ8 header connection on the MPU in the same fashion, check the pins and wires running into the connector, look for bent connectors inside the Molex connector or wire fraying. Check the boards and components for corrosion on each IC leg, transistor or diode or anything that might cause out of spec resistance.
If you already done this, it might be time to break out the logic probe and dmm and start looking at the CPU, PIA, RAM and or ROM on the sound board Also probe the PIA at location IC36 on the MPU board...