Hi,
the network connection status information is not directly attainable using LabVIEW's built in vi's. You're going to need to find the windows API calls to get to this information.
Start by looking at google for network status monitor. Ethereal (http://www.ethereal.com/) do a network information product, which is open source, and this might give you some ideas on packet sniffing information etc.
Essentially you'd be looking for an ActiveX automation server, or ActiveX control that would acheive the functionality you want, then this could easily be incorporated into LabVIEW. Even a .net assembly would usually be incorporatable.
Check around the web for example code and downloadable controls etc.
Hope that helps
Thanks
Sacha Emery
National Instruments (UK)
// it takes almost no time to rate an answer