I am unable to get AlphaFour Ver3 (dos based) to open under Windows
2kPro. It has always worked previously, until the other day. Now when
I try to open the program, I get an error screen (generated by Alpha)
that says "Lan Error - Adapter Malfunction - Please Reboot". 
Rebooting doesn't help. Nor does unloading every running program. I've
reinstalled the program. Still no help. Any ideas on what the conflict
might be?

Try this:

goto start, run, type regsvr32 %systemroot apppatchslayerui.dll hit
enter
You should receive a message that says the DLL has been successfully
registered.

Right–click the icon of Alpha Four 
Click Properties. 
Click Compatibility tab. 
Click Run this program in compatibility mode and try selecting Windows
95 and apply the setting
Hope that works for you.