I installed First Encounter a few days ago and was playing around with the graphics settings. To put it simply, I maxed all of the settings and then used the nVidia control panel to apply anti-aliasing and anisotropic filtering to it as well. At first all seemed well but then I'd get the odd random crash here and there.
The crash itself resulted in showing a square tiled pattern of nonsense graphics with a repeating sound and I'd have to reset the machine. After it did this three times in subsequent reboots I deleted my PersistentSymbols.ini from the game's scripts folder in order to reset all of the graphics settings. I also reduced the nVidia control panel options.
Since then I've been able to play through the training level without crashing but haven't yet spent that much time in game since. I don't know whether my resetting of the graphics settings did it (the only amendment I've made to the default settings it chose for me was to manually apply a 1680x1050 resolution with field of view set to 100 for widescreen (by manually editing the PersistentSymbols.ini file).
My machine is two years old now and I suspect it was my GPU that was the cause of the crash. Unfortunately my GPU model (GTX 260) is known for hard reset crashes so I may consider changing it next year. I can't pinpoint the exact setting which was making it crash and I don't know if it is fully fixed but my initial thoughts are that I was overstretching it with the 32-bit progressive textures with all texture sizes maxed out.
So, try tweaking your graphics settings and see if it helps. Delete the PersistentSymbols.ini file if you need to reset them (it makes the game think it is on its first startup.
