There are 4 parts to the IP address game that need to be addressed before you can access the internet. The first is the IP address that each device gets, the second is the netmask to ensure that you are in the right subnet, the third is the gateway to which all of your packets are routed and the fourth is the DNS that does the name => IP address conversion for you.
When you use DHCP, all 4 pieces of information are sent to your machine and configured. If you switch to static IP on your machine alone, you have set all 4 pieces of information AND you have to go into the router and specifically exclude that static IP or a range of them from the possible IP addresses that could be given out by the DHCP server.
To that end, what you should do to set a static IP address is NOT to do it on the end device, but rather at the router end. You go into the DHCP server and used a fixed (from the DHCP servers perspective) address for a specific device based on it's MAC (not to be confused with Mac) address which is globally unique.
So in the DHCP server/router you say device with MAC address xx:xx:xx:xx:xx:xx always gets IP address 192.168.1.6.
The DHCP server will now hand out a fixed IP address, but also the other 3 pieces of information as well to ensure your network/Internet connectivity continues to work..