So what seems to be happening is PE6 tries to open a file and redraw itself, but it stalls for some 20 seconds and allows the desktop to show through at that time.
PE6 has likely made a call to open a file, Windows has said 'hang on a second', then spent much longer than a second waiting to see if something it thinks should be there is, until finding it isn't, and then allowing things to continue as they should have done.
In the meantime, something else within Windows has noted PE6 has been stalled and has marked it as "Not responding"
That would also explain why the issue affects both laptop and desktop if both have used whatever has now gone AWOL.
That would tend to support some networked or previously mounted drive, or resource not being accessible, things grinding to a halt until Windows decides it can proceed.
That would also explain why it only affects PE6 and not other apps because it's only PE6 which has previously accessed whatever has gone AWOL, not those other apps.
The 'off the top of my head' things I can think it could be are a networked drive, NAS or similar, a USB hard disk or memory stick, perhaps previously used for backup, or maybe something Bluetooth or wireless related.
Bluetooth is notorious for pretending devices are present when they are not. They are only revealed to not actually be present when referenced and Windows has checked if the other side is there or not. Windows has to stall while the Bluetooth stack tries and make a reconnection to something no longer there, only discovering it isn't after some time, when the Bluetooth stack times out. The more devices it thinks are there, but aren't, the more waiting for timeouts there will be, the longer a stall may last.
Have you used any Bluetooth devices, any of which may have created virtual COM Ports ? It might be worth checking Device Manager to see what COM Ports it is showing.