Not sure if your original TalkTalk disc is Vista compatible, depends when you received it. Maybe worth checking.
However not normally a problem to set up new PC assuming that your router is connecting to the internet okay. The router holds your broadband connection settings so these don't have to be reset.
Not sure what you meant by directly connecting new PC to wall socket. No need, just connect the new PC, using a network cable, to the Belkin router and it should automatically create the network connection for you allowing internet access.
However if you have any problems just comeback on the forum and I am sure there will be all the help you need