I think this could go on like a guessing game for ever and a day. I really think, now, that the quickest way to determine the cause would be to take the Tower and monitors to another location be it your house, the local PC engineer or similar and try it there. If you don't get the problem then it is local to the house. The electrics are 30 years old so there could very easily be a fault there. At least have the earthing system cheked, Sounds a bit like fluctuating electrical power to me but only guessing. But then if you get the problem at a different location then it means it is the PC. You said earlier "the new system was installed by a pro technician, it wasn't an upgrade of an old system, so i wouldn't have thought insufficient power supply would have been an issue."
Does that mean it was a new Dell PC set up in the house by a technician, or did the technician actually build the PC? I guess this has been asked earlier in this thread but if the PC is a new Dell has it always had this problem? If not when did it start and can you do a system restore to a date before it happened. All this providing you establish it is the PC and not the location that is causing the problem!