I have a new iMac (Mountain Lion) and have been setting up my mail accounts. I use gmail and have it forwarded to my Mac mail. I get a LOT of newsletters, etc so have set up a LOT of mailboxes in "Rules" so that only the really important stuff lands in my inbox. I noticed the other day that no new mail was coming into my inbox, but mail was going into the other mailboxes. I also realized that some of my important mail was coming in (I have sounds set up for family members and I could hear the sounds going off) but not showing up in the inbox. I found the mail in one of the mailboxes I had set up. That mailbox had very specific rules for 2 email addresses but the mail that was showing up in it had nothing in common with either of those addresses. Nothing I did would change the new mail from skipping my inbox and going into that mailbox. So I emptied it, deleted it and restarted mail. The next set of new emails that came in once again skipped my inbox and, much to my surprise, went into a brand new mailbox that appeared out of nowhere with the same name on it as the mailbox I had deleted!!! I have done this several times now - and every time I restart Mail, that deleted mailbox reappears and the new mail all goes into it. It doesn't show up in the list of mailboxes in "Rules" but there it is, with my new mail, while my inbox stays empty.
Any ideas or suggestions? This is driving me nuts!!!

I should point out that all of the other mailboxes that I have set up in "Rules" are working fine. Only the mail which has no rules assigned to it (my important emails) are going into the "nonexistent" mailbox.