In order for us to better investigate this issue you need to add a little more non-personal information.

Please add the troubleshooting information to your post To find the Troubleshooting information:

• Open Help (or click on three-line-icon and select Help)
• Choose Troubleshooting Information
• Use the button Copy to clipboard to select all. Do not check box "Include account names"!
• Paste this in your post.

Please also add the result of these troubleshooting steps to your post

• Does Thunderbird work in TB Safe mode (see Thunderbird Safe Mode)?
• Do you use anti-virus and firewall software? What is the version?

Application Basics

   Name: Thunderbird
   Version: 14.0
   User Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:14.0) Gecko/20120713 Thunderbird/14.0
   Profile Folder: Show Folder

             (Local drive)
   Application Build ID: 20120713141924
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Crash Reports: about:crashes
   Memory Use: about:memory

 Mail and News Accounts
   account1:
     INCOMING: account1, , (none) Local Folders, plain, passwordCleartext

   account2:
     INCOMING: account2, , (pop3) HTTP:110, plain, passwordCleartext
     OUTGOING: smtp.mail.yahoo.com:465, SSL, passwordCleartext, true

   account4:
     INCOMING: account4, , (pop3) pop.mail.yahoo.com:995, SSL, passwordCleartext
     OUTGOING: smtp.mail.yahoo.com:465, SSL, passwordCleartext, true

 Extensions
   Test Pilot for Thunderbird, 1.3.9, true, tbtestpilot@labs.mozilla.com

 Important Modified Preferences

   Name: Value

     browser.cache.disk.capacity: 1048576
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size_cached_value: 1048576
     extensions.lastAppVersion: 14.0
     font.name.monospace.el: Consolas
     font.name.monospace.tr: Consolas
     font.name.monospace.x-baltic: Consolas
     font.name.monospace.x-central-euro: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.tr: Calibri
     font.name.sans-serif.x-baltic: Calibri
     font.name.sans-serif.x-central-euro: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.sans-serif.x-western: Calibri
     font.name.serif.el: Cambria
     font.name.serif.tr: Cambria
     font.name.serif.x-baltic: Cambria
     font.name.serif.x-central-euro: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.tr: 14
     font.size.fixed.x-baltic: 14
     font.size.fixed.x-central-euro: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.tr: 17
     font.size.variable.x-baltic: 17
     font.size.variable.x-central-euro: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 17
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     network.cookie.prefsMigrated: true
     places.database.lastMaintenance: 1505095574
     places.history.expiration.transient_current_max_pages: 104858
     plugins.update.notifyUser: true

 Graphics

   Adapter Description: Intel(R) HD Graphics Family
   Vendor ID: 8086
   Device ID: 0116
   Adapter RAM: Unknown
   Adapter Drivers: igdumd64 igd10umd64 igd10umd64 igdumdx32 igd10umd32 igd10umd32
   Driver Version: 8.15.10.2559
   Driver Date: 10-21-2011
   Direct2D Enabled: false
   DirectWrite Enabled: false (6.2.9200.22164)
   ClearType Parameters: ClearType parameters not found
   WebGL Renderer: Google Inc. -- ANGLE (Intel(R) HD Graphics Family) -- OpenGL ES 2.0 (ANGLE 1.0.0.1041)
   GPU Accelerated Windows: 0/1

I think I have McAffee firewall protection and possibly AVG and CC Cleaner as well.

Unsure about Thunderbird Safemode.

I think before we do anything else you need to update your version of Thunderbird. V14 is just to old and may in itself be the cause of the issue. It does not have any of the modern SSL information that may be needed to connect to Yahoo

Download and install from getthunderbird.com. This will do an upgrade for you.

On another note. I have no idea what to make of the first account. I can not see how it could possibly work given it has no server name.

Thanks Matt. I downloaded the latest version but still get the same error. Now what? Any ideas?