Tod:
It is unlikely that the hardware inside the GPSR that generates the voice prompts has failed.
To troubleshoot your unit and try to get it working again, do the following:
1) Press and hold the SPEAK key - this will enable you to adjust the volume up to the highest setting.
2) Ensure that you have enabled the voice prompts on the appropriate settings page of the GPSR. I can't recall exactly how to do this, but it should not be difficult for you to figure it out - you can download (free) a complete user manual for your SP III from Garmin if you don't have a printed copy handy.
3) Physically inspect the hole that the cable goes into on the top (back) of the GPSR to make sure that the pins are not dirty or damaged. At the same time, have a look at the plug that goes into this hole - use a magnifying glasss - to make sure that there is no damage to the connectors on the plug.
4) Try connecting your SP III to a 'known good' power cable with a speaker built into the end of it. This will allow you to determine if the problem is within your power cable or within your GPSR.
My guess is that you probably have a hardware problem with your cable - either one of the pins is damaged, or perhaps a wire is broken inside the cable as a result of many years of use and flexing.
Michael