My Belkin wireless G router does not seem to work any more. If I connect my router to my DSL modem, I am not able to make a connection to the internet via the router to my iMac. However, if I connect the dsl modem to the iMac directly, then I am able to connect to the internet seamlessly, I have tried to power down the dsl modem and the router a number of times, but with no luck. I have even tried a soft reset of the router (via the browser interface using ip address : 192.168.2.1), but no luck via this path either.

So if you connect the computer directly to the modem , it works .
That means your modem is working properly. Your ISP is DSL connection. Now connect the modem to the router and the computer to the router. Open the router xet up page and change the settings of the router according to the type of connection you have.
There are 2 types of connection in DSL.
DHCP and PPPOE .

Click Here for step by step instructions

Have you checked the setup of the router? Could it not be set correctly for your modem? Check your manuals from both the DSL provider and the Belkin router. Routers do go bad, but I would check all of the settings before replacing the router.