Assuming the igniter to that burner is working properly, the best bet is that the burner is clogged an not getting gas. This will require removing the burner to clean it and the venturi valve (which is part of the burner), as it can become a haven for spiders.
Since removing the burners on a Ducane grill can be a bear to do. I have included a link to your Owner's Manual, in case you have misplaced yours, that you can download and print for future reference. Pay particular attention to the Annual Maintenance section. As it will walk you thru how to remove and clean the burners.
Answers & Comments
Assuming the igniter to that burner is working properly, the best bet is that the burner is clogged an not getting gas. This will require removing the burner to clean it and the venturi valve (which is part of the burner), as it can become a haven for spiders.
Since removing the burners on a Ducane grill can be a bear to do. I have included a link to your Owner's Manual, in case you have misplaced yours, that you can download and print for future reference. Pay particular attention to the Annual Maintenance section. As it will walk you thru how to remove and clean the burners.
http://help.weber.com/manuals/ducane/2008%20Manuals%20pdf/20529916_030308.pdf
I hope this helps you and thanks for choosing FixYa. Happy Grilling!!