So, now I have played a bit more with one of the machines.
I have tried to boot in "Fail safe" mode, and no luck; same behavior.
Tried to execute lazarus.exe from a Console window. No output.
Tried appending --debug-log=name_of_log_file.txt , but it just outputs an empty file.
The exe files was identical on a working and a non-working machine.
I have tried downloading the "Advanced Password Generator" (
http://wiki.freepascal.org/Lazarus_Application_Gallery#Advanced_Password_Generator ) to test another application. It does not start either.
Tried 64 and 32 bit. No difference.
Did run Dependency Walker again. The bitness of loaded DLLs and Application matches when it is 64 bit (everything is 64 bit).
Disabling/changing antivirus, or excluding a directory is unfortunately not an option. It wouldn't surprise me much, if this was the cause, despite the logs showing nothing relevant.
I cannot afford to spend more time on this issue. So we just agreed, that the users will use the application on a computer, where it works - even though it bugs me a lot, that I could not find a solution :-( and everything, besides Lazarus applications (and Lazarus), seem to work fine.
The application I wanted to run, is a small app that a student at our company wrote. If it turns out they will use it a lot, we will probably just buy new PCs for the users. Or I will rewrite it in a language that I know (it is 450 lines) - then I would be able to support it as well.
Thank you everybody for your suggestions - you are a very friendly and helpful community.
If I can give back with a bug report, or a stack trace (that I can make in a simple way) - I can do that.
I can follow up in my spare time, but I can not borrow the PCs much more.