Domain redirect issue

Hi
I am a newbie to wordpress and I would like to get some help in following matter. I have a domain and a hosting linked to it with a static page. Now I wanted to use it also as a place to keep my blog, so i created subfolder on the server where I installed my copy of wordpress. Bought a new domain and directed it to lets say domain1.com/wordpress.

It works fine, but all the links on the wordpress show as domain1.com/wordpress/… not newdomain.com/…

I tried changing both URLs in settings to point to newdomain.com but then I could not login to wordress admin page (I was getting only my front page with no CSS). I had to edit DB in order to restore old links. And now the fields with the links are grayed out in Settings.

Can You tell me how to correct this? How to make the WP to apper as it was on newdomain.com not domain1.com/wordpress?
Thanks in advance!