Hp media center m8000 was freezing so did a manual

Try unplugging it and plugging it back in. If then you get no power try plugging it into the wall directly and check the power cord unplug it and plug it back in (From the back of the PC). When you press the power button put your ear to the PC and listen for a metallic click. Most PC's use a small micro switch to tun the power on and off but they do make a small noise if you listen.
If all this does not work the power supply is probably bad. If it is under warranty then send it in. If it is not under warranty you can replace it yourself all you need is a half hour and screw driver. From the picture above it looks like a regular tower so any ATX power supply will do.
But if you are not the get your hands dirty type any pc tech place can replace it for you and should only charge you $40 for labor plus $20 to $40 for the Power supply itself. By the way when shopping for a power supply you do not need that 1000w with the flashing neon lights. Get one that is around 700w look at the fan I personally would spend the extra money to get one with a large 4 inch fan with lots of air flow money worth spent in my book. The large fan can get more air flow for a cooler pc and since the fins are larger it can do it with less RPMs so you have a quiet little box in your corner.
Hope this was helpful