The short answer is "no." DJ gave a great explanation above. The bottom line is that regardless of how you set your TV and DVD player, a widescreen DVD disc is displaying a picture that is wider than your TV screen.
In order to see the entire picture from left to right, the areas with no picture just show black bars at the top and the bottom of the screen (also known as "letterbox")
Depending on your set, you may be able "zoom in" until the screen is filled from top to bottom. However, you will be cutting off the picture to your left and right.
The only way to quote "see the whole picture on the whole screen" on a regular TV is to use a non-widescreen DVD disc. This does NOT mean you are really seeing the whole picture! As DJ explained above, this simply means you have a "pan and scan" disc. In other words, you are allowing the DVD producer to choose what parts of the scene are not visible.
Since you have a nice large screen, my personal recommendation would be to stick with the widescreen and live with the black bars. You might be comfortable sitting a little closer to the screen. You're still going to get a fairly large picture, and you won't miss anything! -Bruce