Sounds like an ailing power supply. If you're using a power strip, surge protector, or uninterruptible backup power supply, remove those and connect PC directly to a wall outlet.

You can try this:

1. Power off and unplug power cord from both rear of PC and from the wall
2. Press/hold power button on PC for ~30 sec
3. Reconnect power cord to rear of PC
4. Connect power cord to wall

Does it boot now?

Thank you RoHe for replying to my message I did as you mentioned, i disconnected PC plug from UPS and connected it directly to wall outlet. It turned on after second attempt of pressing power button. I reconnected it back to UPS and pressed power button, it turned on. So i don't know if it's the power button or the power supply. Is it normal for the LED on the back of the power supply beside cord to be turned off while the PC is plugged to an outlet, because mine only turn on when the PC start. So what do you think?

Did you press/hold power button for ~30 sec with power cord removed from PC as I suggested?

IIRC, the green PSU LED is only on when this model is powered up. If this model has a built-in self-test (BIST) button near the  PSU LED on the back, power PC off and unplug the power cord from the rear. Wait at least 15 sec and then plug in and press/release the BIST button. If LED stays green for 3 sec, the PSU is probably OK.

Next time it won't boot, look at the front power button. What color is it, and steady or blinking?

When was last time you replaced the motherboard battery?

1. Boot PC and immediately press F2 to open BIOS setup
2. Copy down all current BIOS settings to be safe
3. Power off and unplug
4. Press/hold power button for ~30 sec
5. Open case and remove motherboard battery (details in Service Manual)
6. Install fresh CR2032 3-volt coin cell battery ($~2)
7. Close up and connect only mouse, monitor and keyboard
8. See if it boots immediately now when connected directly to the wall outlet

If you get any error messages when booting after replacing the battery, reboot and press F2 to go into BIOS setup again. Make sure all BIOS settings match what you copied. Be sure to save the changes -if any- before exiting setup.

Yes i did as you mentioned pressing button for 30 sec with power cord removed from PC. I also unplugged the power cord from the rear, waited 15 sec and plugged back PC cord, pressed the BIST button. The led turned green and fans started spinning, when i released the button green led turned off and fans stopped spinning. When the PC doesn't boot, the font power button stays black, when it turns on after second or third attempt it's white and steady. I haven't replaced the motherboard battery, this PC i got two years ago. I will try to remove motherboard battery and see what will happen. Again thank you so much for your help. I very much appreciate it. Have a good day.

Start with the battery, cheap and relatively easy.

If that doesn't help, you can consider the PSU or the power button next...