Mac is connected to network but internet still won't work?

Question

before chirstmas my internet was working perfectly fine, but it went down, like none of the familys laptops worked, the ipad didn't, none of the ipods, my mac or my iphone, since it was chirstmas we couldn't ring up to get it fixed.. however just after new year the router seemed just fine everything started working again expect for my mac, it says i'm connected to my wireless network but i can't access the internet, i've tried restarted my router countless times, it does nothing, i've tried to delete my network, i've tried deleting airport, nothing has worked.
fed up of having to hopspot with my iPhone it's costing me a bomb, as i'm a graphic design student at uni i need the internet:/

Answer 1

Run /System/Library/CoreServices/Network Diagnostics (this is the program that gets offered to you when you try to connect to a web site in Safari when you are not connected to the internet.  It's really hard to find -- seems to be invisible to spotlight -- so if you get it to launch from Safari you should save it in your dock.)
What you will probably see is that the first couple of lights are green (which is why it says you are "connected" to the wireless -- you are) and then the bottom 2 or 3 lights are yellow or red.
Follow the troubleshooting instructions in NetworkDiagnotics and you may just get things to work.
What I suspect is that you have no DNS, because your router isn't handing out DNS.  To simply bypass that problem, go into your network preferences and hit the "Advanced" button and then the DNS tab, and add a manual DNS server.  If your ISP has given you the address of a DNS server, use that one.  Otherwise use 8.8.8.8 or 8.8.4.4 -- those are google's DNS servers.