The documentation for w32-register-hotkey says it is [h-] so I used that. Using [H-] does work as long as I change the variable before calling w32-register-hot-key like so:
(setq w32-lwindow-modifier 'hyper)
(w32-register-hot-key [H-])
(setq w32-pass-lwindow-to-system nil)
Thanks.