Lots of Dell equipment has a surge protect circuit in the power supply. This will lock the power supply and prevent it from starting. The way you reset it is unplug the power supply and let it sit. All capacitors need to discharge to get the supply to reset. After that it will work just fine till it sees another surge again and trips the lock out circuit. I do agree with everyone as well caps are usually and issue in these but it this case I am betting lock out circuit. I have "fixed" hundreds of dell computers by resetting the power supply.
Interesting video however. I work on Dell equipment professionally all day long I have run in to this issue in servers, optiplex, Insperon, Latatude, laptops, printers, and monitors on SFF, USFF, and micro resetting power supplies is normal operation after storms. The issue is so prevent we don't even go on site any more until a reset is tried. I have run it to is so much now that I have to think it is intentional rather then a bug. In the 240 Watt SFF power supplys why is there so much circuitry in there when all I get is 240 Watts of ATX power.
Also if you open up some of the SFF or USFF power supplies. They are FAR more complex then they need to be especially for the wattage's that they run in In the server world I have even run in to power supplies that hand shake to the mother board and I have had a main board refuse to start with out a DELL power supply installed in the server. I have had a T330 Server not boot with a brand new Corsair 850 Watt ATX PSU. Tried it cause the server went down over the weekend and could not get parts till Tuesday. Plugged the Dell Supply in to the server and off it goes. I have to imagine that I2C is coming out the of supply to the board some where
By the way the reset interval is not weeks it is however over 30 Seconds to a minute. You can some times speed up the process hitting the power button a few times to get the supply to try and start it pulls the charge out of the caps faster. If you unplug and re-plug to fast supply does not discharge and the reset does not happen.
Which is also why I used FIXED in "quotes" because you are not really fixing anything but it does bring the unit back in to service and the user is happy again so as the tech you did "FIX" it in the users eyes.
Just some interesting observation from a Tech that works on this stuff all day long.
Zen