My iMac won’t finish booting up

If I power it on and give no keyboard input, it boots you about halfway (progress bar under the Apple logo is 50%) and then get a “no” symbol (circle with reverse diagonal line through it).

If I power it on and hold the shift key to try to activate safe mode, the same thing happens.

If I start it and hold Cmd-R for about 15 minutes, the Apple eventually appears and the progress bar goes to about 90%. I then get the disk utility, but none of the options will run.