Mail + account setup properly, mail fetching starts but emails don't appear

Question

I'm using Apple's "Mail" program for the first time (after having used Eudora for 20 years).
I successfully:
- Imported all my Eudora mailboxes + contents
- Set up my email account settings
- Connected to the Internet and sent myself a test email
HOWEVER, when I "Check Mail," and watch the "Activity" window, it seems to show my computer successfully connecting to the email server and all my pending emails being "fetched," *but when the fetching is complete, they have not appeared in my Inbox!* I don't get an error message or anything like that -- everything seems to be working exactly as it is supposed to be. The only problem is that the emails simply don't get downloaded to my computer, even though the Activity monitor seems to show them doing so.
I finally was able to open the "Mail" program's "Account info" window (it's not easy to find!), and it reveals that the same 15 pending emails are still awaiting me on my ISP's mail server, even after repeated fetchings of them. While watching both the "Account info" window and "Activity" window, I once again click "Get All New Mail," watch the 15 emails seemingly getting fetched, but when it's all over (3 seconds) -- they're still on the server and still not on my hard drive.
I don't know how to fix this glitch because the program doesn't seem to think anything's going wrong!
Obviously I must have mistakenly clicked some setting that prevents the emails from being downloaded to my computer, but I've scanned the Preferences pane and every single menu option dozens of times, and can't find what I've done wrong.
Any suggestions? i came so close to making the migration without any major problems, and on the very last step something went awry. Very frustrating!

Answer 1

As to "Rules":
I'd already investigated that many times. The only "Rule" was a disabled unchecked rule about "Get Apple News," a subscription to the Apple RSS feed. However, at your suggestion, I also just now deleted it, and then refetched the mail afterward, with the the exact same unchanged result -- still nothing arrives. (Tried several times.)
As for the "Junk" mail setting:
The only two boxes checked were "Enable Junk Mail filtering," and "When junk mail arrives, mark it as junk mail, but leave it in my Inbox." So, even if the incoming mail had been marked as junk, I still should have seen it in my Inbox. Also, Junk's "Advanced" box is greyed out and unavailable to click. All that is moot, however, because I just now unchecked "Enable Junk Mail filtering," so the entire Junk preference pane is now greyed out and disabled; and even after that, when I check for new mail, I get the exact same problem as before, unchanged.
As to "POP" vs. "IMAP":
My account is supposed to be a "POP" account, and it is indeed shown as being a "POP" account in the Accounts preference pane.
But here's a new observation I just made:
When checking mail, in the left-hand sidebar on my "Inbox" window, at the bottom is a section called "MAIL ACTIVITY." When I check for new mail, in this activity box it says "Incoming messages, 1 of 24" then "Incoming messages 2 of 24" all the way up to "Incoming messages 24 of 24," with a blue progress bar filling up below it -- +exactly as you would expect if the mail was successfully being fetched+ (it's up to 24 messages on the server now). Yet after all that, after all 24 are shown as being fetched -- *there is still NOTHING new in my !nbox*! (Or in any other mailbox.) And in the previously mentioned "Account Info" window, afterwards all the emails are still shown as awaiting me unfetched on the server.
So mysterious and frustrating! Every setting and activity seems to be exactly as it should be, with the sole problem that nothing ever actually shows up! The answer is probably so simple, I can't see it.