IMPORTANT! WordPress Custom Fields Problem

I am having a major problem with adding WordPress custom fields in this website I am building. The site has been moved twice so it's now on the third server. What's happening is on the first server it was installed on, I could add Custom Fields and Values all day long with no problem. Now when I go in to update some of the Values and add new Custom Fields, and update the post, no change has been made. I don't have a ton of experience using WordPress so I have no idea where to start.

I guess I will start Googling the issue but if you have a fix or a suggestion, I'd love to hear it! As always, your help is greatly appreciated.