I don't mean to keep adding so many posts, one after the other, but I've been working on this all day and I think the problem may have been that once I checked the emails on the POP account XP computer, they automatically deleted them from the inbox on the IMAP account Windows 8 computer because the emails were being kept on the 'server' ie. the POP account. I'm not sure if this is the reason all the time, though, for the disappearing emails.
So, I decided to try to open a POP account on Outlook 2013 again. The first try to set up a POP account worked a couple of days ago, but like I said, for some reason the emails were not going to that account. I set up another one today right from the account settings tab, and it worked. At least for now. The emails are going to both computers, and the emails are staying in the inbox of the Outlook 2013. I'll just have to see if it keeps working. I'll report back, hopefully with news that the emails are staying in the inbox.
