When I got a Chromecast, I had a hell of a time getting it to actually work.  Turns out there was a random setting in my router that was preventing proper communication.The router I have is a Medialink Wireless N router (Wireless N Broadband Router – 300 Mbps – 2.4GHz – 802.11n to be exact).  After wasting some time searching Google (with no luck) I shot their support an email (on a Friday night).  To my surprised they got back to me early the next morning!!  On top of that, their suggestions worked!!  Here is their response:

AP isolation would prevent the Chromecast from communicating to your computer or iPad or phone that is being used to set it up. So, yes you need that disabled in the router.

Apart from that, the only other thing I suggest is trying different security settings to see if the Chromecast needs one particular type or another.

Open an Internet Browser (ie: Internet Explorer, Mozilla Firefox, Google Chrome, Apple Safari etc.)

Type the IP Address of the router into the address bar. By default it is
Enter the Username and Password. By default they are both “admin”.
Click Advanced Settings
Click Wireless Settings > Wireless Security
Change the Security Mode to “Mixed WPA/WPA2-PSK”
Change the Algorithm to “TKIP&AES”
Click Apply

Emphasis is mine.  Everything I found online seemed to suggest that AP isolation was the issue. However it turns out that the real solution to my problem was the Security mode (and/or Algorithm).

So, mad kudos to Medialinks support for both answering extremely quickly as well as having the actual answer to my problem!