If I only test my pages with MS Internet Explorer and I have not tested my pages with other browsers but my HTML and CSS passed the validation of W3.org, is it a guarantee that my website will display correctly with other browsers, that I have not test with my pages?
Most of the browsers follow W3C basic rules. So once it passed at: http://validator.w3.org/ , I think you are good to go. Try this: http://www.anybrowser.com/ .
No buddy, that wont work. Each browser has different workings and different css support. One thing right in one browser doesnt guarantee that it will be right in other browsers too, this same logic works for scripting language also. You can only be sure after checking the performance at different browsers.
I agree with rajku, You need to check your website with other browsers also, because different browsers different results.