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.
If you can't find where compinit is called, try running zsh -x 2>zsh.log (exit the shell as soon as you see the prompt) then look for the compinit call in zsh.log
Do I need zsh/complete and zsh/computil for normal completion to work?
Yes, you do need zsh/complete and zsh/computil, if you want any completion at all.