If your iPad is not on iOS 5 (Settings > General > About > Version) then the only way to upgrade it is by connecting it to a computer's iTunes - only when iOS 5+ is installed can future updates be done directly on the iPad.
Updating to iOS 5+ : http://support.apple.com/kb/HT4972
You can't upgrade to iOS 5 without using a computer and iTunes. After you upgrade to iOS 5, you can do future upgrades OTA.
You can take your iPad to an Apple Store and ask them to update it for you, but without a backup, you will lose everything on the iPad. You can always download your paid content again - or most of it anyway depending upon where you live.