I think it would be helpful if your software was easier to install.
I couldn't figure out an easier way of installing things as they are present now, and truly, it doesn't appear to be a miniBB problem... if your web server works OK and configured properly, then it takes a couple of minutes to install miniBB.
It would be great to know about your configuration, i.e. what kind of Windows, Apache and PHP versions do you have.
Also, do you run any other PHP apps on your WAMP configuration?
I know about the redirection problem Windows-based configuration could experience (and most likely you have a redirection problem), and for this we have an option in setup_options.php, which looks like this by default:
You have to de-comment it so it looks like:
If it's enabled, the script will use an intermediate HTML template for redirection, instead of a header.
Also, you may have a mistake in the cookies configuration. The cookie is not being set, that's why you are redirected to the same login screen 'cause the script couldn't authorize you.