Can you access the webdialer URL from the same PC using the browser?
If you can, then i've seen issues with clicktocall (the executable) being blocked on the PC by agressive personal firewall/security software, like Symantec Endpoint Protection. Something to do with the executable trying to bind or create a port or miniport. Try it on a PC on the same subnet but without the security software.
Alternatively, If you can't even access the webdialer URL from that PC then you either have a network connectivity problem between PC and CallManager, or your webdialer service is not activated. Possibly a proxy is getting in the way.
The Webdialer service only needs to be activated and running on one node in the cluster and in general can run on the Publisher.
On my cluster (version 8.6) the webdialer URL is https://x.x.x.x/webdialer/Webdialer - you can find out the URL by looking in "directory" after logging into CCMUser and looking at the URL's directory where you can click on extensions. I think it has changed over major releases.