Thank you for the suggestions!
But, running the installer as administrator didn't change anything for me, the error is exactly the same.
And when I try to 'start as services', it tells me "Can't install service: the system cannot find the file specified", then, "Cannot run server: The specified service does not exist as an installed service".
BUT! I found a good work-around while I was looking in the configuration... I just disabled "check server's TCP port before starting"... since I know that nothing is using port 80, I figured maybe only the check was faulty.. and yep, now that it's no longer checking if port 80 is in use, it works perfectly ;) The problem was just in the error reporting, I guess!