I seldom turn my monitor of on purpose, but then I seldom turn my computor off on purpose. I do, however plug them each separately into a surge suppressor that has a switch so that I can hit the surge cable switch and shut everything down.
The main reason for this in my case is that we get quite a few thunderstorms here, and it's sometimes necessary to shut everything down in a hurry when the back yard starts to glow and shoot off sparks.
If you can find the serial number for your computer, you can quite likely find a place at the Dell website (look in "Support") where you can enter the serial number and they will tell you when you bought the machine and if it's still under warrenty. They should also be able to give you a list of all the components that came with it.
Of course, Dell's response does depend on you're having registered it when you got it (?).