here is a possibility;
I had this same issue with a site i was building for a client, and it turned out that the client had their icontact account changed by icontact to FDO (Forced Double Opt-In) because they sent an email that had too many bounces. icontact changed their settings without them knowing, and that setting also turns off any possible API connection. Which means they could not use any API setting until they called into icontact support and cleared the whole thing up.
Also this took 3 different calls and emails to iContact for them to actually figure out and confirm that this was the issue.
Problem has since be changed and the plugin has been working since.. with WordPress 3.3.2 and Chrome