@PANINE
How to you know that it is actually in sleep mode and not dead? Which would not be unusual for a PC this old if it still has the original 10-plus year old hard drive in it.
How have you tried turning it on? Have you held down the power button for 30 seconds or longer, seen the light go out, and then pressed it again?
Have you disconnected the power cord for 5 minutes or more and tried this again?
I am a volunteer and I do not work for, nor represent, HP