I have no problem connecting my DSM-520 to media server over a wireless network, but I can't get it to access the internet.
The function "test internet connection" fails.
I have defined the GATEWAY and DNS IP addresses same as my other home PC's which work fine.
What could be the problem here ? Should I do any changes on the router to forward some ports to the DSM-520 ?

Could possibly be a firewall enabled on your router that is preventing the DSM-520 from getting access to the Internet. Check your router logs.

My router is an old SpeedTouch Pro which I wasn't aware that even had a firewall, but I will check to make sure.
I also have a Netgear wireless router configured as a bridge, so I wonder if there could be a firewall running on that device ?

I changed the network setup on the DSM-520 to use DHCP instead of static IP and the problem is now resolved.