New users can't vote on questions or answers. Even when they ask a question, they aren't able to vote on the answers to that question. If they click the up arrow, they get a dialog box telling them that they won't be able to vote until they obtain enough rep. What they can do is accept the answer. However, despite the grey check being right below the voting icons, many get confused and need coaching -- enough so that it's fairly common on new users' answers to see a helpful comment explaining how to click the check mark to accept the answer. I ran in to a couple already today.
It would be an improvement if the action of clicking the up arrow could automatically coach them to accept the answer if it answers their question. You could put a button in the dialog (that should be pretty easy), or even do something fancier like highlight the check with a tag explaining what it does.