Anyway - Map and Map-Administrator run now but only if I avoid loading a third party plugin. As soon as the plugin loads both programs crash - which doesn't happen on any other PC I tried. The CER report details show the following message:
<InnerException type="System.MissingMethodException"><Message>Methode nicht gefunden: "!!0 System.Array.Empty()".</Message><StackTrace><Method>
It seems that the plugin was compiled against .net 4.6 but the .net runtime is lower than that. You can find a more detailed explanation here (reply by Alexandru).
That is a bit odd as Map 2017 itself requires .net 4.6 and therefore should not start up or run without 4.6 - but it does. When I checked the version of .net framework under "Installed Programs" it showed 4.6 but also 4.5:
The problem seems to be with language pack and / or registry settings. Here are the two keys where the values don't match:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\NET Framework Setup\NDP\v4\Full\1031\Version = 4.6.00081
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\NET Framework Setup\NDP\v4\Full\1033\Version = 4.5.51209
Map 2017, SP1