Printer problems include power problems, which can be daunting especially if you are trying to print important documents. There are several factors that can cause the printer to not power on, including hardware problems. Through trial and error, you can determine what is causing the power problem with your HP printer.
Plug the printer's power cable into the power outlet. Press the printer's power button and wait for the power light indicator to flash or start blinking. If the power light does not flash, press the button again. Note that some HP printers will take a while before they power on, so you have to wait for the device to initialize first. Don't hold down the power button too long--it may power on, and then turn off.
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Disconnect the printer's power supply from the power outlet ("power supply" refers to both the power cord and power module) and check for any visible damages. If the power cable is damaged and the printer is still under warranty, you may have it replaced by HP. Note that the power cable is attached to the "power module" (the one that looks like a laptop adapter). Detach the power module from the printer, and then connect the power cable into a power outlet. If the green light on the power module does not light up, contact HP to have it replaced.
Plug the power supply to the HP printer once again, and then plug the power cable into the power outlet. Ensure that the power cable is attached properly to the power module. If the printer still does not power on, try plugging the power cable into another power outlet. If the printer powers on this time, the problem is with the power outlet.
Unplug the USB connector located at the back of the printer, and then turn the printer on. If the printer powers on without the USB cable, it may be causing the printer to not power on. Consider replacing the USB cable if this is the case.
If the printer still does not power on after doing these steps, consider replacing the printer with a new one. If it is still under warranty, go to the nearest HP service center and inquire if you can have it replaced.