Mail not receiving new email messages.

Question

The Mail application on my 2006 MacBook has stopped retrieving new messages. The Mac is running 10.5.8, and the Mail is version 3.6. I have not made any changes to the mail preferences in years. I have two email accounts configured: my Gmail as well as my university email account.  Comcast is my internet provider. About a week ago, the incoming email was slow to update. I would click "Get Mail", and it would pull in only 4-5 emails at a time. I would re-click "Get Mail" several times until all the new mail was retrieved. But for the past 4 days, no new mail is coming in.  When I click on "Get Mail", the wheel next to both accounts spin like they are working, but nothing happens. There is no error message given (such as "no internet connection"). I have tried the mailbox "rebuild" on both accounts several times, as well as rebooting the computer. (When in doubt, reboot!).
The outgoing emails I send from Mail are being received by the recipients, so I know the connection is working in that direction!  The Comcast internet is working, and I can log in to my Gmail account through the web and view my emails there just fine. I'm also receiving the new emails on my iPod Touch. So, I know there are new emails, but they are not coming to my MacBook.
Any ideas?

Answer 1

Thanks for the suggestions, BDAqua. Unfortunately, the new mail is still not coming in.  I am still able to send mail out through Mail (I did another "test" mail to myself, then checked it on Gmail.com).
A couple of comments & questions (to make sure I was doing things correctly):
The "Connection Doctor" had all green dots. So, that all looks OK.
What do I do with the Mail folder and Envelope Index file that I had moved to my desktop during the Safe Boot? Right now, they are just still sitting on my desktop while in normal start-up mode.
When you said "redo to Rules", I moved the two files you mentioned into the trash. Is this what I was supposed to do? Should I "empty trash" to make sure they are gone?
After I ran through your suggestions once, I did the "safe boot" again and re-ran the Disk Utility "Repair Permissions". Of the things it found, none seem to be Mail related. But, just for kicks, I'll paste the results log below.
Any other ideas? I am able to get my mail through Gmail.com, so it's not the end of the world if I never get this fixed. Just annoying!
Here is the log of results from "Repair Permissions":
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/DVD.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/FRSettings.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/FRSources.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/Movies.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/Music.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/Photos.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/Podcasts.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/CoreServices/Front Row.app/Contents/PlugIns/TV.frappliance/Contents/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Permissions differ on "System/Library/PrivateFrameworks/BackRow.framework/Versions/A/CodeResources", should be -rw-r--r-- , they are lrw-r--r-- .
Warning: SUID file "System/Library/Filesystems/AppleShare/afpLoad" has been modified and will not be repaired.
Warning: SUID file "System/Library/PrivateFrameworks/DiskManagement.framework/Versions/A/Resources /DiskManagementTool" has been modified and will not be repaired.
Warning: SUID file "usr/sbin/pppd" has been modified and will not be repaired.
Warning: SUID file "usr/sbin/vpnd" has been modified and will not be repaired.
ACL found but not expected on "Applications/Utilities".