I don't see Network Connect, but I do see a line that says "Host Checker Not Required"
You may have an incorrect bookmark, or you may have attempted to access the VPN by starting to type cuvpn.colorado.edu in your address bar but selected a longer address recommended by your browser.
You should only access the VPN by opening https://cuvpn.colorado.edu. This is the address that should be specified in any bookmark you've made for the VPN.
Mac: Network Connect client fails when I try to open it from the desktop/applications folder
You must make sure Java for Mac is installed and also enabled. Java is not installed by default on Mac 10.7(Lion) or 10.8 (Mountain Lion).
Note: If using Mac 10.7 (Lion) or 10.8 (Mountain Lion) you need to go to Java Preferences and check the Enable applet plug-in and Web Start applications checkbox before logging into https://cuvpn.colorado.edu, as shown in the image below.
To open Java Preferences:
Open a Finder window.
Click on Applications located on the left sidebar,
Open the Utilities folder.
Double-click Java Preferences.
Log in using your Identikey username and password.
In the Client Application Sessions section click the Start button.
Custom VPN
I tried to access my custom VPN but got the standard version
Make sure to press Enter, or the "Go" button, in the "Sign In" line of Network Connect after entering the custom VPN URL. Network Connect acts like a mini-browser to get to the actual sign-in page, and you have to tell it to go to the URL before you can login there.
Read more about connecting to the network with a Custom VPN.