The game can be run in "fullscreen" at the 4:3 aspect ratio, but it usually takes some tweaking of your GPU settings and/or the monitor's menu. The first thing to try is deselecting GPU scaling or auto-rescaling or whatever it's called in your GPU software. If the option is there and you can turn it off, the game should run fullscreen but there will be black bars down each side to "fill" the area of the screen that the game doesn't use. For ATI/AMD gfx cards though, some more recent versions of the software won't let you deselect auto rescaling unless you set your desktop to something other than the monitor's native "recommended" resolution. I don't know about nVidia.
If you can't turn off rescaling in the GPU software you can try going through your monitor's settings menu to see if there's an option in there regarding rescaling and try setting the monitor to *not* rescale stuff.
On my old installation I had to change my desktop resolution, make the necessary changes in the GPU software, then change my desktop res back to the recommended settings; when I did that, the options I was just tinkering with would "grey out" but my selection would "stick" and kick in if I lowered the resolution again. Then I used a program called Display Changer to lower the resolution automatically whenever the game was running. It worked as far as maintaining the 4:3 aspect ratio so stretching of the graphics was not a problem. It was just a real headache getting it all set up, and unfortunately I still couldn't take screenshots with the Res Fix enabled because the game would either freeze up or crash totally.
So... in the long run, for me, not being able to take screenshots was more of a dealbreaker than anything else and when I reinstalled on the new computer and tried the Res Fix it was still a persistent issue. What I'm using right now instead is
Conus' SH3GWX Widescreen Mod although I've done a bit of tweaking to make it compatible with my other mods and to personalize it to my own tastes.
http://www.subsim.com/radioroom/showthread.php?t=170191
The mod reworks the graphics to give a (roughly) 16:9 aspect ratio to the 2D screens that would be stretched out otherwise. I think they are done in 1360x768 or thereabouts, they just get rescaled to 1920x1080 on my system and there's no need to stretch things out horizontally to fill the screen.