Does it work if you copy the study files off of your mapped network drive and onto your Desktop? If not, ignore the next paragraph and give us a call so we can figure out what the problem is.
For testing and previewing studies directly from your computer, Lighthouse Studio actually starts a web server on your computer to mimic the true survey experience. It sounds like you may not have all the permissions necessary on the mapped network drive for the web server to access the files it needs. If that doesn't work, have your IT department double-check that your firewall is allowing LighthouseStudio.exe to access the network drives.
Feel free to give us a call if there are any further questions. (http://sawtoothsoftware.com/about-us/contact-us)