I cannot open settings on my Ipad.

Try closing the Settings app/icon completely : from the home screen (i.e.not with Settings 'open' on-screen) double-click the home button to bring up the taskbar, then press and hold any of the apps on the taskbar for a couple of seconds or so until they start shaking, then press the '-' in the top left of Settings to close it, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar.

If that doesn't work then you could try a reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.

You may have a corrupt backup. If restoring the device and then restoring to your backup does not eliminate the problem, I think that's a pretty good assumption. If you can't alleviate the problem any other way, you may have to restore to factory settings and then resync all of your content. That is painstaking and will cause you to lose all of your data, but it may be unavoidable if you want to get the settings app to work again.

Before I would take that course of action, I would update the iOS software to 4.3.5 if you haven't done so already and maybe that will help.