When you click the airport icon on the top toolbar of your Mac's desktop then wait a few seconds does it show a list of available wireless networks?
If so can you tell me what happens if you choose your Sisters wireless connection, Does it ask for a password XXXXX does it give you an error?
Can you click the apple icon then choose system preferences and open Networking.
When it opens can you then select the airport and then tell me what it says?
Can you go to System Preferences then Network and open AirPort then select TCP/IP and make sure that the option to Configure IPv4 is set to Using DHCP and let me know what it was set to.
Can you try to renew your IP Address lease by pressing the button on the right side of the TCP/IP settings window to request a new IP address from the Router.
If that does not work can you unpluug the router itself for 30 seconds then plug the power back in and wait 2 minutes then try to renew your IP again and let me know what happens.
Do you know if you can use her machine to access the router so you can check some settings?
You said that they have two wireless networks, So can you tell me if you get the error on both when you try and renew your IP Address?
If so can you try goinf to System Preferences then Network and opening Locations then choosing New Location and naming it something you wilol remember such as your sisters name and then then try configuring your network one more time under the new location you just created.
If that does not work then I would assume there is some type of MAC blocking turned on on the router and we will need to try and make a few small changes to see if your machine can get access.
Let me know how you get on with the new location.
In that case can you give me the model of her router
Can you go to a machine that can get online through the router then click open a Internet Explorer Window and type the gateway address in the following format http://192.168.1.1/ then hit enter to open the routers login page.
When prompted to login Just click Ok then on the left can you go to the Advanced tab and then click Mac Filters on the left side and then next to Access Control can you set the mode to disabled using the drop down menu and then save your changes and let me know if you can then connect your Mac after about 2 minutes?
If you get disconnected can you just follow the link you should have been emailed and it will bring you straight back here so we can continue.