Can not share the internet via wireless
I noticed an Issue in our Company on some of the 2011 27-Inch iMacs were sometimes the Ethernet-Adapter failed.

If your Ethernet Adapter is not connected to the Internet, your Mac won't share the connection via Wireless, because there is no ethernet/internet to share.

You may try it : Plug in the ethernet cable, share the ethernet via wireless.
If it starts to share ( like in the first picture ), plug off the cable and watch what happens. I can't reproduce it here, but it will probably change to the grayed icon as seen in picture 2.

Other reason could be a failure of the Router were the internet is coming from.
The Sharin panel is simply sharing "Internet Access" so if you are connected to your Intranet ( Home Network ) but not to the Internet (www), then it will also not work like you expect it. The Icon will stay gray, until you are sure you have access to the Internet.

And If you really have Internet Access via the Ethernet Adapter, then there is something wrong with the Mac. 
You could Try :
- Reset PRAM (at start sound press CMD + ALT + P + R)
- Reset SMC (press power button for a couple of seconds when the cable is unplugged and the mac is turned of)
- Restart the Ethernet Adapter -> go to the system preference pane for the network, click on the ethernet adapter -> go down to the little gear and click on deactivate service, wait a minute, then click on activate service and the ethernet should start properly.

This could happen if the Ethernet Drivers are not working properly and in some cases it can happen, that those crash. I had that Issue on a older Mac Pro that always refused to connect, when I restarted the router and the mac got a new IP.

So there are as always many reasons, that could cause the problem.
just comment if you are getting any closer to the problem.
Then we are able to help in a more specific way.