I found a solution after lots of trial and error. Thought I'd come share before I went to bed. Hopefully it works for some of you.
For some weird reason, Internet Explorer seems to be causing the issue. First off, follow Omrakos' instructions in this thread on how to Disable Proxy Settings and Dial-up Connections. After you've done that:
1) Open Internet Explorer.
2) Go to File (Alt+F by default)
3) If Work Offline is checked, uncheck it. If it's not checked, check it then uncheck it.
Voila, working Launcher!
If these steps alone don't fix the Launcher for you, try deleting your Battle.net folder (found in C:\ProgramData) and your Cache folder (C:\ProgramData\Blizzard Entertainment), then follow the steps.
Please be sure to post in this thread if this fix worked for you. GL!
If the IE fix doesn't work for you, this is one that I have gotten to work:
1. Open cmd.exe as administrator.
2. Open your D3 launcher.
3. When you get the "Checking for Updates" bar, type [ipconfig /release] (minus the ) into your command window and press Enter.
4. Your launcher should open up. If it does, go back to your command window and type [ipconfig /renew] (again, minus the ).
5. Check to make sure your launcher is connected. If it is, you're good to go!
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