My Mac won't connect to the Internet, but my other devices can.

Hi!
Registered just for this question. My Mac which is on snow leopard and hasn't had its software touched in a few weeks is suddenly not able to connect to the Internet, but it can find the wifi! What's weirder is all of my other devices connect fine. Out of the 5 years we have owned this iMac, we never had this problem.
I've tried a few basic things
-rebooting the Mac, and modem, keeping them off for around 30 minutes
-turning airport off, then on
-resetting safari
-googled all over the place
-registering here for help!

I don't think it's my modem, I'm using it now on another device. What's wrong with my Mac and how do fix this

Thanks!

First lets rule out your Mac will it connect anywhere else ? ( meaning can you take it to a friends house or a Starbucks etc etc and connect)

Firstly, welcome.

1. Does the problem just affect wifi?
2. does the problem remain if you connect your Mac to your router by ethernet cable?
3. Have you install all the Software Updates since installing Snow Leopard?

Please post details about which mac you have.