Previews aren’t always 100% accurate, so you could actually activate the new theme and test from there. If that’s not an option, it’s safer to copy your current site to a staging server and test it out there. Most likely some of the paths in the stylesheet are pointing to the wrong folder. If you inspect the element where you expect a background with dev tools, it should show you whether the image was found or not. If not found then double-check what folder everything is in.
Many stylesheets use relative paths like /styles/background.jpg rather than spelling out http://example.com/theme/styles/background.jpg so if your WordPress blog is in say a subfolder like http://example.com/blog/ and the stylesheet is using a relative path, you’re telling WordPress to look in http://example.com/blog/styles/ for the background image when in fact that is not the right folder. In this case you would need to change the stylesheet to point to ../styles.background.jpg (the ../ says go up one level).