I've had this same issue multiple times running not just CX3 systems, but AX4-5, CX4, and older CX300 series systems as well.  The fix is, when you input the IP of the system into the browser, append it with /start.html at the end.  For example, [URL] will bypass the pluginchk nonsense that it seems to hang on.  Also running x86 win7 here, JRE 7 update 45, latest firefox, chrome, and IE, and i get the same issues if i don't type /start.html after the IP.
We have a CX3 running Navisphere 6 and I'm having an issue accessing the web interface.  I can connect no problem if I remote to an older system (Server 2003 R2, IE 7, Java 6 Update 5).  But on my desktop running Windows 7 x86 with Java 6U45 (we can't use 7 due to other incompatibilities), if I try to connect with Firefox or Chrome (latest version each), I get directed to a page called pluginchk.html. I can sometimes log in with IE 10 but it crashes a lot and performance is pretty sluggish.  Is the issue with FF or Chrome the fact that they're disabling (or making it hard to run) Java? Or is the incompatibility with Windows 7? I'm not sure where to start looking. Has anyone had success with newer O/S and Browser with Navisphere 6?  Thanks,
Navisphere 6 Pluginchk.html