well if you try to use satic IP, you must make sure to provide valid subnet mask/gateway/DNS for the connection to work properly. if you are not sure what settings to use, then while you are connected to the internet, open a command prompt and type in "ipconfig /all" note down subnet mask, gateway, and DNS Server ( usually two DNS Servers ), put that in your TCP/IP Settings and it should work.
on the other hand, if you have a router and wish to use a static IP, you can tell your router to assign the same IP address each time to your machine. it is called STATIC DHCP, and it is assigned from the router configuration. but you need to know the MAC Address of your network adapter. to get the MAC Address, also open a command prompt and type "ipconfig /all" and look for physicall address, that is also another name for the MAC Address. then open your router configuration window from your browser, type in 192.168.1.1 which is usually the router's IP ( sometimes 192.168.0.1 or something else ) and type in user/password, that should be admin/admin by default and then goto Static DHCP settings, enter the IP address and MAC address combination you want to set, then you propably have to disable and re-enable your adaptor so that it will pick-up the new IP Address you assinged it. hope this helps!