If you are willing to install a third party free app, there is a simple trick which can bring back the Favorites button back as well as the Favorites pane on the left. Microsoft still kept the keyboard shortcut (Ctrl+Shift+I) to show the Favorites on the left. So you can put a shortcut in your IE Favorites bar that runs a script in any language and sends the Ctrl+Shift+I keystrokes.
You can use VBScript etc too but I prefer AutoHotkey because it doesn't provide any confirmation or warning prompts in IE.
1. Download the ZIP file attached to this post and extract the AutoHotkey script (.AHK file) anywhere e.g. Desktop or Documents folder.
2. Download and run AutoHotkey installer from this page:
http://ahkscript.org/download/. You will need AutoHotkey installed so you can run this script without any confirmation prompts.
3. Create a shortcut to the AHK file you downloaded by right click -> Create shortcut and copy-paste the shortcut in the folder called C:\Users\<your user name>\Favorites\Links\. (The folder inside Favorites may be called Favorites Bar instead of Links).
4. Now open IE. You will get it as a button/shortcut on the Favorites bar.
5. Since it's a shortcut, you can right click it and assign it the Favorites star icon from C:\Windows\system32\imageres.dll. Then you can drag it all the way to the left, next to the Add to Favorites button. It performs exactly like the button to toggle the Favorites pane.
The only catch of this is that the Favorites pane does not automatically close when you click outside it. I switched from using the mouse to the keyboard shortcut Alt+C to get used to this horrid change.
Note that this workaround has nothing to do with Classic Shell. Classic Shell is not responsible for anything that happens to your computer from use of the recommended third party software.
The result is something like this:
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