Homepage appears badly by guest user (not registered)

Hello everyone,
I found a problem these days: The homepage of my e-commerce done with woocommerce is displayed correctly when logged in to the site, but if a user enters as a guest, the homepage automatically sees bad.

jewelrybijouxforerika.it

I tried deleting the file index.php to understand what was going on and the user logged site disappeared, but if I connected to the guest user site was still there!
What do you think I could have done? Considering that I suspected was the program for the cache but instead also eliminating the problem remains.
Many thanks to those who try to help me, are days that I feel!