I'm sorry for having sent mail directly to you.
And I'm even more sorry for having sent nonsense. I wasn't
concentrated enough. So I'm trying to do better now.
When Your emacs is loaded, AUCTeX is merely required but not
completely set up, thus emacs does *NOT* know about a mode-map called
TeX-mode-map (neither is LaTeX-mode-map known).
Therefore the error occurs.
Please try the following:
UseQuote:> (require tex-site)
> (define-key TeX-mode-map 'f1 'my-new-binding)
(define-key LaTeX-mode-map [f1] 'whatever-you-want)))
When opening a (La)TeX document now, it should work. AUCTeX is first
loaded and the (La)TeX-mode-map is set up,
then the hook is run and voil.
The thing you used before switching to AUCTeX had worked for it was an
`emacs-built-in-mode' and tex-mode-map was therefore known.