I believe that to create a new folder or a new subfolder, you must first, within the unnamed tab which I will refer to as the "folder tab", click once to select the folder or mail account which should be parent to the new folder or subfolder. You can also right-click on the desired parent folder or parent account and then choose "new folder" or "new subfolder" from the resulting contextual menu.

This is exactly the process I'm using, yet a new folder does not appear in the Inbox folder list. It doesn't matter whether I use he right-click method or File > New Folder from the main menu,

Thanks for the clarification. Sorry, I should have assumed you were correctly creating a new folder in the first place. In looking at this again, I think the most likely reason you can't create a new folder will be that Thunderbird is unable to log into your e-mail account. For example, perhaps your username or password is not entered correctly in the Thunderbird settings. Further explanation follows:

It would help narrow down the problem if you can check if this problem is limited to creating new folders in your e-mail account, or if you are also unable to create new folders in your "local folders."

In the Thunderbird "folder tree" in which you are presented with your various folders, (Inbox, Drafts, Sent, etc) you should have an entry named "Local Folders" and also an entry whose name is your e-mail account address. These entries represent the "root level", respectively, of your local folders and your e-mail account folders.

If you right-click on the "Local Folders" root entry then you should be able to create a new folder within the "Local Folders," and likewise, right-clicking on the e-mail account root entry should allow you to create a new folder within the e-mail account.

If you are not able to create a new folder within "Local Folders", then perhaps your computer has run out of disk space, or, perhaps there is some other weird problem happening with your Thunderbird installation.

If you ARE able to create a new folder within "Local Folders", but you are NOT able to create a new folder within your e-mail account, then perhaps your e-mail account has run out of storage space, or perhaps your e-mail account is simply configured to deny you permission to create a new folder, or, perhaps there is a configuration problem whereby your e-mail account login settings (POP or IMAP settings, port numbers, username/password, etc) are not all set correctly per the instructions published by your e-mail account provider.