What sort of router are you using? Most domestic routers use addresses starting 192.168.... It is unusual to find a home network using addresses in the range your are quoting.
As well as setting up the IP address, have you set up the correct sub-net mask, gateway address and DNS address? When address setting is automatic, all four of these parameters are set up for you by the DHCP server in your router. When you go for a static address, you need to set all four manually.
Another thing to watch is whatever address you choose, it should not be within the range of addresses that the DHCP server is configured to allocate. You will need to check the address range used for DHCP by logging on to the router and checking what its settings are. If you do set a static address in the DHCP range, it is possible that the router will allocate the same address to another computer, which will cause you major problems.
Make sure that the address you allocate for your static address is in the same sub-net as your router. Once you have set up a static address, try connecting to the address of your router. Don't use an alphabetic URL, use the numeric address of the router. If it tells you the address is not reachable, then you have got your static address or the sub-net mask wrong.
For home networks it is normal for the DNS and gateway addresses both to be the same as the address of your router.
EDIT:
Apple tend to be a very closed organisation, and I have not been able to find any specific information about the normal settings used by the Airport Extreme.
I assume that the other computers in your network are getting their addresses automatically. I am not a MAC expert, but in Windows, when the address is set up automatically, the DNS address can be configured automatically or manually. If the address is set up manually, then the DNS has to be set up manually. In Android, all addresses are automatic or all addresses are manual.
Go on to one of the other computers (assuming it is using Windows). Hole down the windows key and press 'R'. Type 'cmd' in the run box. In the window that should appear, type 'ipconfig /all'. This should show you the addresses used by the various network adapters on that computer. Look at the Gateway, DNS and DHCP addresses. Normally these all point to the router. Try putting this address into a browser on a Windows PC and see if the router responds. Hopefully the router will produce a web page on the computer. If it does, use the same address on the MacBook, and see if it displays the same web page. If it doesn't display the page, check the sub-net mask on the MacBook. Try setting the mask to 255.0.0.0 (assuming that the IP address starts 10.0.....). To go much further might need hands-on access by someone who is familiar with the MAC setup.