Magento 1.9.2 checkout redirects to cart, cannot complete order
I have 3 websites, all in Magento 1.9.2. All 3 were working perfectly. Unfortunately, through the years, I was experimental with one of these Magento websites. I used it as a guinea-pig - I installed several extensions (Meetanshi defer JS and Apptrian minify for example). This website now has a problem - During the checkout, after choosing the payment method and pressing on continue further button - the next step 'order-summary' does NOT appear. Instead, the person get automatically redirected to the cart with products. The name, address and info just filled in does NOT get saved, which is irritating as well.
I have worked for days and tried EVERYTHING. Via FTP, I re-installed most of the checkout files.
But no success.
I have disabled all extensions completely.
I also checked all e-mail settings in the admin backend.
Also checked secure-unsecure urls and other settings.
My other 2 Magento stores with exact same version of Magento 1.9.2 and exact same theme work perfect.
I just cannot identify the problem, someone please please help me!