Don't call compinit. That's all you need to do. You might have the call in your .zshrc file, or perhaps another dotfile, or perhaps you source a plugin that calls it. Find out where it gets called and then remove the call. If compinit never gets called, then you'll get the old skool completion system instead.
Do I need zsh/complete and zsh/computil for normal completion to work?
Yes, you do need zsh/complete if you want the old style of completion. Without it, you won't get any completion at all.
zsh/computil, on the other hand, is required only for the "new" (circa 2000) completion system.