I don't believe upgrading will necessarily fix the problem you have with updating. Could you provide additional details in the form of errors, environment, specs etc. so that we can troubleshoot why you are unable to update?
To answer your question, to upgrade from 11.04 to 12.04 you can simply boot from the 12.04 CD or insert the CD while you are logged into your Ubuntu session. Ubuntu will recognise that you have 11.04 installed and offer to upgrade to 12.04, you will not lose any of your installed programs or data, one of the fantastic features of Ubuntu!
Having a separate
/home partition is fine, you will not have any problems.
So either boot from the 12.04 CD and follow the install prompts or insert the 12.04 CD while you are logged in to proceed with the upgrade.