My desktop will not boot up, stays stuck on the logo, then goes dark. What is a disk utility, and how do i find and run it when it won't boot up?

Boot into the Recovery volume (boot with the Command + R keys held down), select Disk Utiity and run First Aid on all volumes of the drive that you can. Then reboot normally and see if there's any improvement.

I think you should make an appointment with an Apple service provider and take your computer in to have it checked.