1) Check The receptacle in the surge protector, that the computer is plugged into.
I have had surge protectors where just THAT receptacle was bad.
"Hmmm, surge protector power on light is lit. Monitor, printer, and router, plugged into the surge protector, has power."
Upon plugging in a table lamp into THAT receptacle on the surge protector, I found THAT receptacle to be bad.
($30+ surge protectors, too!)
2) If the surge protector proves to be good, I would suggest performing a test that checks whether the Power On switch is bad, or the Power Supply, in the computer.
Behind that plastic Power On button, is a Power On switch.
I have found this generic Power On switch fits many computers.
Just an example, to show you what a typical Power on switch looks like,http://www.directron.com/atxswitch.html
The test involves using a jumper wire to bypass the Power on switch, to see if the problem is the Power On switch, or the Power Supply.
Using the jumper wire turns the computer on, (Power Supply on), the problem is the Power On switch.
Using the jumper wire does Not turn the computer on, (Power Supply), the problem is the Power Supply.
This is HP Support, and the main page for the HP Pavilion a705W desktop computer,http://h10025.www1.hp.com/ewfrf/wc/product?product=435558&lc=en&cc=us&dlc=en&submit.y=4&submit.x=5&lang=en&cc=us
Go to the right side, and click on Product Information.
Now click on Product specifications, and then on -
Motherboard Specifications, MS-6577 (Giovani, Giovani2)
(Close the web survey. It's something that can be done without, IMHO)
Scroll to the bottom of the page, and view the motherboard photo, and the motherboard illustration.
Refer to the motherboard illustration
Look to the top right for - CONN1
Now refer to the motherboard photo, and match up CONN1.
It is a white connector on the motherboard. Has 2 rows of 10 socket holes.
The correct name for this connector on the motherboard, is a 20-pin ATX main power cable connector.
This is more information on a 20-pin ATX main power cable, it's respective connector, and the matching connector on the motherboard,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
With the side panel removed on your computer, (Computer Unplugged from power), you will see your 20-pin ATX main power cable, plugged into this connector on the motherboard.
Will resemble the photo to the far right.
Before reaching into a computer, have the power to the computer Unplugged.
Also follow Anti-Static Precautions.
Your body carries Static electricity.
Static will fry out (Short Circuit) the delicate hardware components inside a computer.
Relieve your body of Static BEFORE handling any computer parts, (hardware components), that you are going to install, and BEFORE you reach inside your computer.
Computer unplugged from power, computer case open, work on a table. TOUCH the metal frame of the open computer case, to relieve your body of Static electricity.
Should you get up, and walk away in the middle of working on your computer, upon your return be SURE to Touch the metal frame again.
Best method is to use an ESD wrist strap, (About $6), and connect the alligator clip to the metal frame.
Electro Static Discharge ]
Observing the photo to the far right, the procedure is to use a jumper wire from the Green wire, to ANY Black wire.
The main power cable is plugged in as shown.
One end of the jumper wire goes down into the socket hole with the Green wire, and the other end goes down into a socket hole with ANY Black wire.
[ The Green wire is the Soft Power on wire. Abbreviated as PS-ON.
ANY Black wire is a Ground wire.
You are making a circuit with the jumper wire, from the Soft Power on wire, to ANY Ground wire ]
The wires that go down into the main power cable's connector, have plastic insulation on them.
At the end of Each wire is a metal terminal connector.
(They resemble this metal terminal connector,http://www.mcmelectronics.com/product/28-9410&green=13639529671&utm_campaign=MyBuys&utm_medium=Recommendation&utm_source=prod&utm_term=28-9410
The metal terminal pin is pretty far down in the socket hole.
For this reason, you have to ensure that the jumper wire is going down in the socket hole, (Right next to the wire that is already in the socket hole), and goes down in far enough to touch that metal terminal connector.
I usually state using an insulated wire, but am now going to concede, and advise what many state to use for a jumper wire.
A paper clip.
The paper clip is straightened out, then bent into a U shape.
The center of the U is wrapped with electrical tape.
The taped part of the paper clip 'jumper wire', is then held with your fingers, and thumb.
You may also wish to don a glove, on the hand that holds the jumper wire.
There will be a spark.
The voltage is 5 Volts DC.
Two D cell batteries used in a flashlight produce 3 Volts DC.
I would lay the computer on it's side, opening up.
Easier to access the 20-pin ATX main power cable's connector.
(Won't hurt a computer to lay on it's side, and be powered up)
Computer plugged into power, insert one end of the U shaped paper clip into the socket hole with the Green wire.
Now bend the paper clip if necessary, and insert the other end into ANY socket hole with a Black wire.
Make SURE the paper clip is touching the metal terminal connectors, down in the two socket holes.
Computer comes on?
Bad Power on switch.
Computer does Not come on?
Bad Power Supply.
The Power Supply used is just an ordinary ATX style of Power Supply.
Common in over 80 percent of PC's out there, and readily available.
The Wattage is 300 Watts.
The shape, and size of the Power Supply's case is approximately,
A) 6 inches Long
B) 6 inches Wide
C) 3-1/2 inches Tall
Make sure it has a 4-pin ATX +12 Volt power cable,http://www.playtool.com/pages/psuconnectors/connectors.html#atx12v4
(Also abbreviated as P4 ATX 12VX1)
Newer Power Supply's have an ATX main power cable, that it's connector can be used as a 20-pin ATX main power cable, (Which you need), or a 24-pin ATX main power cable.
This is one example of a Power Supply that will work in your computer, and is reliable, while economical,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=1389575&CatId=1078