Your client is quite right, the site should load in all versions of 6 to 8 of Internet Explorer, Firefox, Chrome, Safari and Opera on both PC and Mac. Your whole first page takes forever to load whichever browser I look at, I didn't even get the header to show after more than 20 seconds in Firefox on a fast connection, much too long.
I think you have way too much going on in that first index page. I know clients often push to have everything they have on the first page, but you really can't see the forest for the trees. You have 7 different flash and javascript slideshows plus a drop down menu going on at the same time. All these images are being preloaded, plus you are using tables which adds extra mark up to your file, which is why the whole site takes time to appear. Then there is so much movement going on that there is nothing to focus on, and to see all that movement you have to scroll down, the whole thing becomes very confusing.
In design less is often more. I would suggest having your drop down menu and just one Flash slideshow which would highlight the different articles in the menu and maybe your celebs, but combine them into 1 swf file. Then clients could navigate from the menu to the item in which they are interested. You could then put another slideshow on the relevant page highlighting that item.