Well, for one thing, you never closed the <p> tag on the "welcome" paragraph. IE8 (on my machine) has elected to believe that all of the content from that point on lives inside the paragraph and doesn't auto-close until the </body> tag (which is perfectly legal) and is determining the absolute positioning based on the parent element (the paragraph within the paragraph, since you've "closed" the para with another <p> tag). Chrome, on the other hand, closes your original para and opens another one when it hits the second <p> tag, and puts all of the <br>s and the <hr> into that paragraph.
In other words, it's not rendering "properly" in any browser because your markup is incorrect. Your CSS can only work on the HTML you give it, and you've given it broken HTML.