Dell Studio XPS 8100 Desktop

My wife's Studio XPS 8100 Desktop (manufactured 01/04/2011) has been crashing, starting with a flickering screen.  The screen goes blank with a whitish-beige color and is unresponsive.  She turns it off and on, and it still stays asleep.  Holding the power/start button down for 30 seconds used to work for a while, but she no longer can recover her machine from a "deep sleep."  While booting, the computer makes a loud humming noise that is not present when it boots normally.  This was happening under Windows 7 Professional OS and has continued under Windows 10 OS.  

Before, under Win 7 OS, the hard drive began to get slower and slower to the point I was afraid it was failing, and I replaced it along with updating drivers specified by Dell (see previous posts).  There was nothing available for the video card to update.

I read in the community forum that disabling (turning off) the monitor sleep state as well as the computer sleep state was a solution.  That seems to work as long as she never turns the machine off.  If the machine is turned off, as stated in the first paragraph, it takes more and more 30 second cycles to get it to boot normally.

Is there a solution for this problem?  What should I do next?

Thanks,

Creech Newsome

7/5/2016

Liked to never got it to boot this morning,  Finally, it started to boot and I got 7 beeps, it finally booted on the next try.  Looked up Beeps and Error Codes and found that 7 beeps means: