mchartman: No, I just have one core. My computer is really old. I've had it for almost 9 years. Only things I upgraded was the graphics card (looong ago), and I increased the RAM.
What version of the driver do you have? It seems like a graphic card related trouble - the drivers don't quite agree with the way the old unreal engine handles them. Like some features that may be discarded.
You can try two things. Upgrade your drivers to the latest version. We've tested Deus Ex left and right in our testlab, running multiple machines on many different configurations and it gave us no problems at all. And we were running latest graphic drivers.
The reason for that is that video card manufacturers often change their mind about the support for some of the features used by older games - which often creates much confusion since it's really a hit and run with some of the driver versions.
The second thing is downgrading the drivers to the version that was around the game release plus 6 months. There is a profile for Deus Ex in Nvidia drivers with some flags changed.
Another thing you can try (although it's a longshot) is to change the name of the exe file. Add a "Z" or anything else to the filename (not the extension!) and see if it changes anything. That way you will unload any custom flags nvidia drivers have for this game and run it sort of "vanilla" driver-wise. It may help.
Also, try setting the renderer to DirectX.
Alternatively, if all else fails, set the renderer to software. It will look like crap, but if it freezes up then the issue is most likely something else than the GPU.
Anyway, PM me if you have any more problems. It's a great game that shouldnt give too much trouble since it's based on unreal engine.