Logged into the domain but can't ping DNS

I have a computer that is a member of a domain and can log into the domain but once logged in it cannot access anything on the network or even ping either DNS. From another computer on the network I cannot ping that machine either. When logged in locally we ensured that all the TCP/IP settings were correct and the Windows Firewall is turned off.

Where else should I look for the cause of this issue? Why would the computer not be able to ping either DNS but still be able to log into the domain?

Is there another firewall running on the machine? If a second firewall is present and has ping disabled.