Having uninstalled all previous versions of Audacity, I downloaded the latest (.exe) to my Downloads directory, double-clicked it, and got an error message "Application has failed to start because its side-by-side configuration in incorrect. Please see the application event log or use the command-line sxstrace.exe tool for more detail."
OK. To read the "application log" I used ControlPanel > System&Security > AdministrativeTools > EventViewer. In the left pane I chose CustomView > AdministrativeEvents. The very first one was:
Activation context generation failed for "C:\Program Files\Audacity alpha (debug)\audacity.exe". Dependent Assembly Microsoft.VC90.DebugCRT,processorArchitecture="x86",publicKeyToken="1fc8b3b9a1e18e3b",type="win32",version="9.0.21022.8" could not be found. Please use sxstrace.exe for detailed diagnosis.
Googling the forums suggests that (a) this version of Audacity is a debugging version which my Windows installation is not equipped to run, and (b) that sxstrace.exe users need an IQ of about 160. If this is correct, I must give up!