This might be drawing a bit of a long bow, but are the processors in both computers Intel or AMD? Still doesn't really explain anything as even if they are different, you'd think that the way they'd handle co-processor calculations would be consistent between processors. Even so, the errors seem to be random with no particular pattern. Microslop wouldn't entertain a support call, as XP has been sunset a while ago now, but that's probably what they'd put it down to. If the old one could be upgraded to Win 7 +, that might go some way to solving it, but you probably, like so many, just want to leave it on XP, not withstanding the costs of an upgrade licence.
It's probably not worth chasing it too hard, as it does sound to be very random, and I assume that a repetition of conditions causes a different result each time? What about a new blank workbook? Same thing? Anyway, you probably didn't mention this situation to ask for help resolving it, so you might need to just go and kick box with something that you can't rely on too much. The nearest politician maybe?