The problem you’ve got is that your ADSL username / password is hard-coded into the router, so just replacing it won’t work. You’ve two options here.
1) you could add your Linksys behind the Sky router, leaving the Sky router to negotiate the credentials. However, in your case this isn’t going to help you.
2) you can (on the older routers at least) extract the credentials from the router. Look on the skyuser forums, there’s a website where you enter the serial number and it’ll give you the details. Bear in mind that Sky do not support this configuration.
Reason being is that they keep saying ours is knackered and trying to sell us one for £70!!
Ring to cancel, when they ask why, tell them you don’t have a working router. They were giving them away free a couple of weeks ago.