The 'Not enough hotkeys' is only presented after another problem has occurred and you then try PF3 again without restarting FS, sso it's a little misleading. We really need to know what the first message is, but the log doesn't show me anything. Are there any other messages displayed?
First thing to do is to run the PF3 Validation utility, which you can do via the Options #2 button. The onscreen instructions will inform you where the validation log will be written, which I would like you to zip and attach to your post.
You should also reinstall the DirectX Managed Runtimes because depending on the state of your NET installation Windows updates will sometime overwrite the first install of those runtimes.
Next please locate the file named PF3_Register.exe in your main PF3 folder... right-click on it and select 'Run as Administrator'. Wait 30 seconds then try PF3 again