VGA cable arcing against computer case
Most likely you have a faulty ground at the first location, or a mains fault inside either monitor or computer. Another thing that could do this is maybe someone connected the power wrong in the wall outlet. 

Have an electrician check the wall to make sure it's good. 

The best way to measure these is with a volt meter, measure the voltage between the devices, and then between each device and ground (if it really is grounded) if the chassis of either device is more than 0V with respect to ground then that is a faulty device and needs to be replaced. Make sure you follow protocol for handling high voltages and treat each device as a live mains wire because you could be electrocuted.