The servers you are on run Firewall software.
So if you find that you can visit the world wide web "EXCEPT" it would seem for your web site, your webmail, your cPanel or just about anything to do with your web site, your IP could in fact be blocked,
this normally happens after you have tried to login to your cPanel, or webmail a number of times and failed.
How to check and unblock your IP:
Please go to your billing account at https://secure.avahost.net ,
Go to menu Support -> Unblock IP
And you will be able to check and unblock your IP address.