The Green LED light you see flashing indicates you have a bad Power Supply.
Computer unplugged from power, computer on a table, computer case open, observe Anti-Static Precautions.
Clean the inside of the computer out with a can of compressed air for computers, (Or may take two, and a few Q-tips), and replace the Power Supply.
Supporting data:
HP Support > Pavilion 523w desktop computer > Main support page,
http://h10025.www1.hp.com/ewfrf/wc/product?product=90859&lc=en&cc=us&dlc=en&submit.y=9&submit.x=7&lang=en&cc=us Click on > Solve a problem > Start Up/Shutdown/ Power > Power Management
Click on the + sign to the left of > Power supply light is on or flashes
Replacing a Power Supply,
1)
http://www.fonerbooks.com/r_power.htm2)
http://www.videojug.com/film/how-to-install-or-change-my-computers-power-supplyThe Power Supply is an ATX form factor. The ATX style of Power Supply is found in over 80 percent of personal computers out there, and is readily available everywhere.
It's a 250 to 300 Watt power supply.
Probably made by Bestec, HiPro, or Delta, or some other generic power supply manufacturer of low quality power supply's.
Has a 20-pin ATX main power cable, and a 4-pin ATX +12 volt power cable.
Plus the usual amount of 4-pin Peripheral power cables, and a Floppy Disk power cable.
http://h10025.www1.hp.com/ewfrf/wc/document?docname=bph07845&tmp_task=prodinfoCategory&lc=en&dlc=en&cc=us&product=90859&lang=en
Scroll down to the illustration and photo of the Motherboard.
Typical 20-pin ATX main power cable,
http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20Typical 4-pin +12 Volt power cable,
http://www.playtool.com/pages/psuconnectors/connectors.html#atx12v4
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