are you using a gmail or other remote calendar that does not support Lightning tasks?

I am using Thunderbird. When I open Thunderbird, the new event/tasks are not active. Not sure what you mean by using gmail or other remote calendar that does not support Lightning tasks. I have a Google calendar and an Outlook calendar but as far as I know they are not linked to Lightning.

Please post your Troubleshooting Information. AppMenu button - Help - Troubleshooting Information

Here is my troubleshooting information:

 Application Basics
   Name: Thunderbird
   Version: 24.3.0
   User Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:24.0) Gecko/20100101 Thunderbird/24.3.0
   Profile Folder: Show Folder

             (Local drive)
   Application Build ID: 20140131124303
   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) incoming.yahoo.verizon.net:995, SSL, passwordCleartext
     OUTGOING: outgoing.yahoo.verizon.net:465, SSL, passwordCleartext, true

 Extensions
   Edit email subject, 2.0.3, true, EditMailSubject@jcp.convenant
   Lightning, 2.6.4, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}

 Important Modified Preferences

   Name: Value

     browser.cache.disk.capacity: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     browser.cache.disk.smart_size_cached_value: 358400
     extensions.lastAppVersion: 24.3.0
     font.internaluseonly.changed: true
     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.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: 13
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: bbcb9f42-8d86-4fa8-ae57-aba758048a0
     network.cookie.prefsMigrated: true
     places.database.lastMaintenance: 1393614194
     places.history.expiration.transient_current_max_pages: 104858
     plugin.importedState: true

 Graphics

     Adapter Description: ATI Radeon HD 5450
     Vendor ID: 0x1002
     Device ID: 0x68f9
     Adapter RAM: 1024
     Adapter Drivers: atiumd64 atidxx64 atidxx64 atiumdag atidxx32 atidxx32 atiumdva atiumd6a atitmm64
     Driver Version: 8.682.1.0
     Driver Date: 12-9-2009
     Direct2D Enabled: Blocked for your graphics driver version. Try updating your graphics driver to version 10.6 or newer.
     DirectWrite Enabled: false (6.2.9200.16571)
     ClearType Parameters: Gamma: 2200 Pixel Structure: RGB ClearType Level: 100 Enhanced Contrast: 50
     WebGL Renderer: false
     GPU Accelerated Windows: 0

     AzureCanvasBackend: skia
     AzureFallbackCanvasBackend: cairo
     AzureContentBackend: none

 JavaScript

 Incremental GC: 1

 Accessibility

   Activated: 1
   Prevent Accessibility: 0

 Library Versions

     Expected minimum version
     Version in use

     NSPR
     4.10.2
     4.10.2

     NSS
     3.15.4 Basic ECC
     3.15.4 Basic ECC

     NSS Util
     3.15.4
     3.15.4

     NSS SSL
     3.15.4 Basic ECC
     3.15.4 Basic ECC

     NSS S/MIME
     3.15.4 Basic ECC
     3.15.4 Basic ECC

When you open the calendar tab, what calendars do you have in the left pane?

I have Home and USHolidays in the left pane when I open the calendar tab.

I figured out my problem. The USHolidays calendar was read only and some how was selected. When I select my Home calendar I can now add new events/tasks. Thanks for your help.