The main window asks me not to interact, but it's not progressing at all - I've left it for over half an hour. My setup is made using Inno Setup 5.5.9. From what I understand the whole process should be automatic, but as you can see it's not working, and I'm not sure what to do now.
In case you want to do this in future (or for anyone else with the same issue who comes looking for this question) I did have a similar issue myself. I have no experience with Inno Setup but I used an MSI file created through a Visual Studio Installer project. It would get stuck on the first screen of the installer.
There should be a stage before the you start running the tests (the same stage when it asks for the file) when it asks for any parameters. I took this as an opportunity to include the same parameters I would use when running MSIExec.exe from the command line if I wanted an install to do a silent install (/qn). Presumably a passive install would have worked as well.
Looking at http://www.jrsoftware.org/ishelp/index.php?topic=setupcmdline, it appears Inno Setup should accept parameters such as /verysilent and /sp. I would expect these to have the same effect.