The replacement hardware came today.
Installed a new socket 370 / socket A CPU cooler:
Now the system can run without overheating and freezing / crashing after just a couple minutes.
Also maxed out the RAM to a whooping 256 MB of PC100 RAM:
This allows Puppy ‘Wary’ Linux to boot and run quite well.
Next will be to start building a Lego chassis to house / support this board and allow for easy prototyping of other components.