If the step down transformer is overloaded, it will become warmer and it's output voltage might drop a little. Switch mode power supplies like those used in a pc have a wide input voltage range, so I doubt that a bit lower input voltage will make a difference. Worst that could happen is that the supply turns off when the voltage is 2 low. Due to that, the load will lower and the voltage will rise again, which might turn the supply on again. Such oscillating would be hearable, and the system would never have time to start up properly. You can buy a cheap power meter to measure the power consumption of your 2 cabinets to see if they stay below 800W.
In my humble opinion, the capacitors of your x2 power supply have simply dryed out.
Sometimes those surrounding the cpu on the mobo become bad as well.
This causes unstable output voltages and the mobo might refuse to turn on due to that.
You have no idea how many working hours the x2 has already. It's not uncommon in an arcade to have things running 14 hours / day.
One piece of advise I would give, don't turn on both machines at the same time with the same switch (Like before the step down)
Monitor chassis have a startup current many times bigger than their working current. So, if both turn on at the same time....