What antivirus are you using? Try disabling that as a test. What is your "home network" that you mentioned earlier?
My home network is a simple wireless network for several home devices. The internet cable is plugged into a wireless router which broadcasts the signal throughout the house. I'm using AVG Free for my anti-virus, and it's up-to-date.
I disabled AVG and restarted e-Sword, but the Module Downloader did not show any modules in the window to download for any of the 6 tabs.
It makes sense that there's a problem with e-Sword "talking" to the internet, but I have no idea what the problem is. All my other programs sucessfully communicate with the internet - web browsers, email client, IM client, anti-virus, etc.