I have installed wp in a subdomain and all seems to be working fine. I have tried two "under constructions" plug ins wich will allow me to see the front end of my site once logged in. If yr not logged in you'll see the under construction page.
How come that the plugins do not recognize me being logged in? Since it occured with 2 plug in's I might be an installation issue and not a specific plugin issue. I guess.
I'm not sure what might be causing your problem between your install and plugin. It sounds like it might be the plugin if you weren't having problems before using it. I wouldn't worry with the "Under Construction" stuff too much since WordPress has a setting where you can keep it from being crawled by the search engines.
My WordPress sites installed with this setting being defaulted to blocking the search engines, but if you need to change the setting, you can by doing the following:
From your Dashboard:
Click Settngs in the left navigation
Click Privacy in the drop-down menu
Adjust the setting using the radio buttons provided
Save your changes
I hope this helps you. Best of luck with your new blog!