How do I get my Macintosh HD drive to save files to its own desktop again?

When you open the Save As dialogue go to Export As and click the arrow on the right to open an expanded view for saving your files, you will now see the Sidebar where under Favourites which list things like Applications, Desktop, Documents etc, these locations are on the drive you are booted from. Under that you should see Devices which lists Drives attached to your Mac, from there you can navigate through the disks to where you may want to save files.

You have a great Mac, get to know it better.

Yes so ok in Text Edit you don't see Export As you see Save As (other Apple apps have Export As) to the right of the you see a little arrow click that so you are on the expanded Save As dialogue with a sidebar as shown above.

Do you have anything listed under Favourites. If nothing is listed go back into Finder and open its Preferences, click on the Sidebar and select which items in Favourites you want to see. Now go back to Text Edit and select Save As, do the things you checked now appear in the Sidebar, if not take the cursor and hover it over the word Favourites, you should now see either the words Show or Hide appear to the right of Favourites, click show to see the list of Favourites you checked in the Finders Preferences. You should be able to see something like this.

I have the same Mac, and it is great, but if you are still having problems then can you provide screenshots

so we can see what you are experiencing.

Ok so if you are not willing to share screenshots to see if we can find a resolution to your problem then the only thing I can suggest is if you pose your question in the Snow Leopard forum, Mac OS X v10.6 Snow Leopard you may get more of an audience.

To my memory I don't think the Save As dialogues have changed that much but I could be wrong I haven't used Snow Leopard in 5 years.