What seems to be the problem with my Acer Aspire

When you want to turn-off the computer hold down the power button until it shuts and it will.

It seems to be hardware problem...
So we have to proceed by elemination here...

Now if you see absolutly nothing on the screen, chance are that you have a memory problem, maybe it just need to be cleaned, maybe you need to change a stick.

First, take away the side cover of your desktop on the side that you can see the interior of the computer then you will see a/some slide(s) cliped-on the MotherBoard, unclip it clean the dust, you can take an eraser to clean the gold connector (you erase them and it will clean the gold). When it's clean, make sure there is no dust inside the slot of the slide and then replace it/them then try to boot the machine. If it work, your a winner, if not you come back to go further in the diagnosis.
Thank you.

Please remove RAM and then check your system if it comes on and off properly with the power button then please replace the RAM. if problem still persist then remove all hardware connected to motherboard likeRAM, PCI cards, CD/DVD ROM and HDD. and then check your system to Give beep and startup and to be proper on and off. if motherboard works proper then connect your hardware one by one and check which one is causing to stop working the motherboard. and even if the problem still persist then there is problem in your motherboard.