When only the product page breaks after adding an extension, it is almost always a JavaScript error, mostly jQuery loaded twice – the second copy drops the VirtueMart cart handler.

1. Open the browser console (F12) on a product page and click Add to cart. An error like "$(...).virtuemart is not a function" or a second jquery.min.js in the Network tab confirms it.
2. Turn off jQuery loading in the slider's own settings – Joomla already loads it.
3. If the slider has no such option, load it only on the pages that need it (module assignment) instead of every page.