The disturbance is most likely being caused by the monitor next to it, so for piece of mind you could try moving the Plus to see if it makes a difference.
My Plus occasionally turns on with a blank screen as well, but I find that pushing the reset switch normally does the trick. It has been doing it pretty much since I got it 6 years ago, but it is still working fine (touch wood). Replacing the PRAM battery may solve the dark screen problem - it seems to have done on mine anyway. Unfortunately the 4.5V AA size batteries are no longer available so you may have to mock up an equivalent. My Plus actually has a 3V coin cell in the PRAM battery compartment, connected by fly leads, and it does the job!
My Plus occasionally turns on with a blank screen as well, but I find that pushing the reset switch normally does the trick. It has been doing it pretty much since I got it 6 years ago, but it is still working fine (touch wood). Replacing the PRAM battery may solve the dark screen problem - it seems to have done on mine anyway. Unfortunately the 4.5V AA size batteries are no longer available so you may have to mock up an equivalent. My Plus actually has a 3V coin cell in the PRAM battery compartment, connected by fly leads, and it does the job!