The case back doesn't need to be screwed down but it does need to be touching the batteries and the case of watch to complete the power circuit for it to function.
Idea's
Make sure you have the batteries the right way up.
Clean the contact points with a fibre tipped pen and some rubbing alcohol both on the module and the case back.
Try both buttons and also an external magnet to see if the display activates.
Be careful not to cross thread the screw ring.
If nothing works consider repair or get in touch with Greg Ratcliff at
gsratman1@embarqmail.com to buy a NOS replacement module.
Good luck.