When I start up Hammer, what I see is some of the Hammer window with whatever window I was previously viewing showing through.

I am running Vista (I know, I know) and haven't set up hammer for Portal... YET. (It may have automagically been done when I got SDK...)

Que...?

I dont really understand your problem but try pressing ctrl+a to reset the windows

I'm using Hammer on Vista and 7 (beta) and it's working fine for me. The problem could be that you have outdated graphics card drivers.
Go to the website of the manufacturer of your graphics card (nVidia, ATI, etc) and get the latest version of their driver.