Thunderbird is a great mail client. But it still suffers from a minor bug that seems to elude it's developers. One fine day the program will lock itself in offline mode for no apparent reason. Regardless of what you do in the settings, Thunderbird will start-up in offline mode and remain so even after answering "yes" to the dialog that pops up asking if you want to go into online mode.
The simple fix for this in windows is to "exit" the program using the "exit" menu item under "file" in the main menu bar. After doing this Thunderbird will start up an reset itself to the proper settings you gave in the preferences area. Using the windows "X" will not help. You must use the exit menu.