Changing the site URL?

Hello, I have everything working on my wp site on http://example.com/wordpress.

I registered another url and pointed it to the wp files so now I have http://new.com.

I changed the settings on the wp admin for the wp URL and the site URL, to http://new.com.

Everything works, but when I try to change http://example.com/wordpress and point it to a different file so I can use that URL for something else completely I get bugs on the http://new.com site. The bugs go away when I point http://example.com/wordpress back to the core files.

I’m just trying to take away example.com from this website so I can use that URL for some other project but it seems to be linked to this website somehow and I can’t figure out why.

Please advise, let me know if you need any other info.

Thanks.