There are numerous possible reasons why an application will run fine on one computer and not on another. These include the influences from other software that is running, different shared code versions (i.e. system and runtime DLLs and device drivers), and differences in the hardware itself. Let's assume none of these very likely reasons is the cause behind your problem..
As far as hardware instability goes, this is actually more of a concern than many people realize. I learned this when I did extensive testing with Prime95 to determine if my system was stable at a given clock speed. Prime95 showed me that even the system boots fine and seems to run quite ok, small memory (or other) errors can creep in and have unpredictable results. Power fluctuations and interference are also a common causes of similar problems.
Therefore, I suggest using Prime95 in it's "Test" (or is it "Benchmark"..) mode to determine if your system is stable. Leave it running over-night. If Prime95 completes ok for about 12 hours, then I'd say that your system hardware is as reasonably stable and the cause is more likely one that I listed, or implied, in paragraph 1.