1) The plastic panel on the front of your computer, is referred to as the Front Panel. (Some manufacturers deem it the Front Bezel)
The cables (Wires) from the Front Panel, connect to a Front Panel header on the motherboard.
A series of pins that stick up out of the motherboard.
The Front Panel header may be separated into two headers.
For most motherboards the Power On switch wires, Power On LED light wires, HarDDrive activity light wires, and Reset switch (If used) wires, usually go to just one of the Front Panel headers.
(If it is the style where two separate FRT PNL headers are used)
You have to locate the wires coming from the Power On switch, and see what pins they go to, on the Front Panel header of the motherboard.
Sometimes the Front Panel wires end in just one connector.
Sometimes these wires are separate, and each one plugs onto a separate pin, in the Front Panel header.
IF, the wires are separate, carefully remove the two wires terminal ends from the pins on the Front Panel header.
[POWER UNPLUGGED from computer. When you are ready to jump the Power On pins with a screwdriver, then plug the computer back into power]
Touch a metal flat tipped screwdriver, that the blade tip is just large enough to touch those two pins, (AND just those two pins), for the Power On switch.
(Inside the plastic Power On button, is a Power On switch.
This is a generic Power On switch for an example,http://www.directron.com/atxswitch.html
The contact you will make with the flat tipped metal screwdriver, will be a brief one. The Power On switch is a Momentary Contact Switch.
There will be a tiny spark. Hold the screwdriver by the insulated handle.
The Voltage is 5 Volts. (DC)
Two C cell flashlight batteries produce 3 Volts. (DC)
I want to show you a generic example of a Front Panel header.
The example I'm going to use is in a Gateway GT5408 desktop computer.http://support.gateway.com/s/MOTHERBD/Intel2/4006160R/4006160Rmvr18.shtml
The white block with pins sticking up is Front Panel header.
Looking all the way to the right of this white block, and under the bottom right corner, you will see the number 2.
This designates that the number 2 pin, is all the way to the right, and bottom.
The bottom row of pins going across are numbered Evenly.
The top row of pins are number Odd.
The top row of pins are numbered 1, 3, 5, 7, and 9, and they start from the Right side, with the number 1 pin..
The bottom row of pins are numbered 2, 4, 6, and 8.
There is No pin 10. These pins also start from the Right side.
In the chart you will see that Pin 6 and Pin 8 are for the Power On switch.
That's the last two pins all the way to the Left, on the bottom row.
If your computer was a Gateway GT5408, these are the two pins you would briefly touch, with that flat tipped screwdriver.
If the wires that come from the Front Panel, (and it is the wires that contain the Power On switch wires), ends in a single block style connector, remove it from the pins.
Just ease the connector straight up, and off.
Now touch the two Power On pins with the screwdriver.
If I knew the computer manufacturer name, and Model Number of the computer in question, I MAY be able to give you a link, showing Exactly what pins to touch in the Front Panel header.
Barring that you jump the two Power On pins with a flat tipped screwdriver, and the computer does not come on;
I would advise using a jumper wire to bypass the Power On switch, to see if the problem is indeed the switch, or the Power Supply.
If the computer comes on (Power Supply starts), the problem is the Power On switch.
If the computer does not come on, the problem is the Power Supply.
This procedure has nothing to do with the actual Power On switch, or the Power On pins in the Front Panel.
You will be using a jumper wire on the 20, or 24-pin ATX main power cable connector.
(Again, I don't know what computer you're referencing to here. The computer could have a 20-pin ATX main power cable, or a 24-pin ATX main power cable)
This is an example of a 20-pin ATX main power cable, and it's respective connector,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
The jumper wire is bent into a U-shape. It touches the green Soft Power On wire, and ANY black Ground wire.
There's more to it than this simple explanation. Should you desire to do this procedure, simply state so in a Comment. (Believe upper right of your page)
Lastly you could remove the harddrive out of your computer, place it in an external enclosure, and plug the external enclosure's USB plug, into any USB port on an available working computer.
This way you could retrieve your financial information, etc. now, and fix your computer when appropriate for you.
An external enclosure is a case that opens into two halves, generally.
The Harddrive plugs into an interface located with the enclosure.
(Interface. Simple explanation - Connector)
The enclosure is closed back up, and it's USB cable is plugged into an available working computer's USB port.
(Any open available USB port. Doesn't matter which one)
Again, I don't know what computer you have, so I don't know if it has an IDE Harddrive, or a SATA harddrive.
One example of a decent external enclosure, used for a 3.5 inch wide IDE harddrive,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=1337265&CatId=2779
(Laptop harddrive's are 2.5 inches wide. Desktop harddrives are 3.5 inches wide. 3 and a half inches)