HP compaq 8710w tries to power up but flashing yellow light and shuts down

Is it plugged in? If so then most likely it is not taking a charge. This could mean your charger has gone bad, the cord leading to it is bad, the cord going to the computer is bad (search for breaks or chewing if you have animals) or the port where you plug it into the computer has suffered damage. This last one is internal as the actual port has come loose where it is attached/ soldered onto the motherboard. You would have to bring it to a qualified repair technician for this. You can also find some online.