Changing WP address breaks site

Forgive me if this seems like a noobish question, I am new to WordPress:

We have recently finished designing a new site for our company using WP. Last night, I redirected my name-servers. When the change had propagated I checked the site and noticed that the name in the address bar is still showing as the ip address instead of my site URL.

I updated all of the hard-coded button links which fixed the majority of the site, but has not fixed the posts as they are generated by WP. After doing some searching I found that I need to update any WordPress address and Site Address in the General Settings section to my actual URL instead of the ip address.

When I make this change it seems to break the CSS stylesheets (or at least does not load them) and it kicks me out of the admin section. When I try to log back in, it fails…perpetually. It locks me out altogether. In-order to fix this I have to update the database records for site_name and home directly, back to the original ip address setting.

Now I’m no expert, but I’m pretty sure something is not right here. So what am I missing/doing wrong?