If you connect your computer directly to the DSL modem, you must use the IP that they assigned you for your ethernet adapter (wether it got it through DHCP or you configured it directly).
Hope you have a good firewall program because you are very vulnerable to attacks when connected like that.
If you connect a router directly between your computer and the DSL modem, then the router uses that assigned IP (it's taking the computer's place) for it's WAN (outside world) port, and you can choose one of those private IP ranges for your LAN (in the house network) between your computer and the router.
The private IP ranges are only for "in the house" networks, and the static IP they gave you is only for communicating with that service (DSL).
I'd give their tech support a call and have them walk you through the setup. That way it should work without guessing.
BTW, your home install package came without an instruction sheet?...odd.