No, I didn't get anywhere with fixing it. What host is your site on? There ought to be a list of e-junkie-hostile web hosts that do odd things with it. Mine was on MS's officelive.com
By default on officelive, it seems that the CSS structure will let you put the module pretty much anywhere you want - but it will either pop the pop up to the middle of the vertical page, or it will pop it into a module frame - but which only displays as much of the cart as you've sized the frame for (which can be a single word in size)
The only workaround that I was able to come up with on officelive.com was to place the module into which I'd put the cart code at the bottom of the screen, size the module to fit around the cart and let the cart appear in a section that otherwise looked blank (because obviously anywhere else on the page except the bottom looks silly with a blank spot.)
You can see an example here http://mygunpurses.com/7036.aspx. It's a little kuldgey, but it works. Note that we also have a stupid "shopping cart" page in the tabs at the top, which takes one to a page with nothing on it but the "view cart button.
I'd have been relatively happy if someone could have told me how to just make the cart appear when that "shopping cart" page was loaded without pressing the button - but I didn't get any traction there either.
Nonetheless the site is making sales, so I guess customers don't find this arrangement too inexplicable.