iPhone has no display My Verizon iPhone was working fine until yesterday, mint condition, no damage. 

Suddenly, there's no display. iTunes detects it but doesn't let me restore with error 3194.

Is there any known fix for this? I just don't understand how it would get bricked sitting on a desk, no jailbreak etc.
Error 3194 is related to a network connectivity issue. Typically security software or a firewall is blocking access to Apple's servers: http://support.apple.com/kb/TS3694#error3194. You can also try connecting to iTunes on someone else's computer (preferably at another physical location as well).

As far as the screen suddenly not working, while not typical it certainly happens. The iPhone is a piece of hardware made from electrical components. Every electrical component made is prone to failure for various reasons. If you can't get it working after a restore, I would highly recommend making a Genius Bar appointment at your local Apple Store.