I’m not able to change the nameservers with the ones that Cloudflare gave me (I know on godaddy you can change the nameservers). If the rest is correct, I believe that would be the problem.
Your nameservers on that domain are currently set to hostcenter.com and not Cloudflare. Back to the original problem, the fact that the site appears as a plain white screen is nothing to do with Cloudflare as your traffic isn’t even going through them.
You will need to change the nameservers to Cloudflare if you want to use their services.