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Thanks for all your replies. Unfortunately something still isn't quite right. I have tried assigning an IP address manually, and in the network settings it is showing as connected with the green light (as opposed to the orange or red light to indicate something is wrong), however it still won't access the internet. When I try and open Safari, it says it can't connect.

Can you ping the router/default gateway.
 
I don't live in the wireless connection world but, it could be a security issue. Try it without a password encryption, (WEP, WAP, WAP2), just to see if it changes things. I have had a problem related to this before.
 
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