I have a Sony Vaio VGN-T170P and have just purchased a new larger HDD
which I have cloned from the existing HDD.  I now need to swap HDDs
and cannot figure out how to open the Sony's case to get to the
existing HDD.

My question is simply how do I get the back or bottom of the Sony
computer open to swap HDDs.  I have removed all visible screws, but
there is still comething at the front of the computer case that keeps
it from opening.  I've searched for Manuals on the internet and Sony's
website tells me to have a professional do it.  Not acceptable.

Manuals. That's cute.

Best bet is to try a laptop computer forum with a dedicated Sony/Vaio
section. Lots of fearless people upgrading and modding their machines.
Often, they post nice pictures and advice:

http://www.talkvaio.com/forum/index.php?showtopic=376