I would first try to get the laptop to work via a hard wired Ethernet connection to the router and then worry about the Wii. If the router is configured correctly the Wii should just work if it is set to use DHCP (Obtain an IP Address automtically).
If the above suggestion about username and password doesn't work then my first guess would be that the ISP has authorized a single MAC address and that is why the laptop works when directly connected to the DSL modem.
If that is the case, then you need to go into the Linksys setup and tell it to always use the MAC address of the laptop (by default it probably uses its own MAC address).
If using WinXP, you can get the MAC address by typing 'ipconfig /all' (without the quotes) in a command prompt. The MAC address is listed as 'physical address' and will have the form: 00-00-00-00-00-00