1) Check to see if the problem is the Power On switch, or the Power Supply, first.
Use a multimeter on the two wires coming from the Power On switch.
Perform a continuity test of the switch.
An economical multimeter can be purchased, for as little as $8 to $12. Available in a multitude of stores. An auto parts store is but one example.
Make notes, and a drawing as to where those two wires go, on the Front panel header, on the motherboard. Then disconnect the two wires, and hold them in your hand.
Set the Function knob of the multimeter to OHM's. (1K, or 10K)
Touch the Positive (Red) probe lead of the multimeter to one wire.
Touch the Negative (Black) probe lead of the multimeter, to the other wire.
Press the Power On switch. (Button)
You should see a brief reading on the multimeter scale. (Or readout if the multimeter is digital)
It is brief because the Power On switch is a Momentary Contact Switch.
No reading? Bad ATX power on switch,http://www.directron.com/atxswitch.html
Good reading? The Power Supply may be bad.
Test the three main voltages coming from the Power Supply.
The Switched-Mode Power Supply, (SMPS), in your computer, is a power converter. It converts AC electricity from your home, or business, into three LOW DC voltages.
The shock hazard is IN the Power Supply's case. Not from the low DC voltages it produces ]
A) 3.3 Volt power rail
B) 5 Volt power rail
C) 12 Volt power rail
Test at the 20-pin ATX main power cable's connector,http://usa.asus.com/Motherboards/AMD_Socket_754/K8VX_SE/
Photo, shows the white, long 20-pin ATX main power cable connector, on the motherboard. No power cable plugged in.
Two rows of 10 socket holes.
(Above the blue Heatsink that sits on the Northbridge chip )
This is a general example of a 20-pin ATX main power cable, and it's respective connector on the motherboard,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
Power cable plugged in as shown in the right photo.
I suggest using a straightened out paper clip, and sticking it down in the socket for the power wire.
This is for the Positive (Red) probe lead of the multimeter, to touch to.
First voltage power wire check:
The multimeter function knob is set to DC Voltage. If just a symbol, the symbol is a dotted line, over a solid line.
IF there is more than one DC Voltage scale, for the Function knob to be set to, set it to the 0 - 50 Volt scale.
The straightened out paperclip, will go down into the BACK of the 20-pin ATX main power cable's connector, RIGHT NEXT to the Orange wire.
Has to go down far enough, to go past the Orange insulation of the wire, and TOUCH the metal terminal down in the bottom.
[Looking at the middle photo, you can see the tips of the metal terminals I am referring to.
Uninstalled, and end not crimped over the wire's insulation, this is what they look like,http://www.molex.com/molex/products/datasheet.jsp?part=active/0002081202_CRIMP_TERMINALS.xml&channel=Products&Lang=en-US
Left side shown, crimps over the insulation of the wire.
The far right side is what you are seeing the tip of, in the middle photo of the Playtool link ]
You can use ANY of the Orange wires you see. ALL are 3.3 Volt wires.
The Negative (Black) probe lead of the Multimeter, touches ANY Black wire.
ALL Black wires are Ground wires.
(Straightened out paperclip, also goes down in the Black wire's socket hole )
Put the straightened out paperclips in the appropriate socket holes, then plug the Power Supply into power. Press the Power On button, and start the Power Supply.
On the DC scale of the multimeter you should be reading VERY close to 3.3 Volts.
Go to ANY Red wire. ALL Red wires are 5 Volts (DC)
Positive (Red) probe lead of multimeter to straightened out paper clip, down into a socket hole, with ANY red wire.
Negative (Black) probe lead of multimeter to straightened out paperclip, in ANY socket hole with a Black wire.
Reading should be VERY close to 5 Volts. (DC)
Go to ANY Yellow wire. ALL Yellow wires are 12 Volts. (DC)
Reading should be VERY close to 12 Volts. (11.5 to 12 Volts)
ANY low reading means a bad Power Supply.
1) If ALL of the LED lights were on at once, they would use less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts of power.
3) A typical Processor can use 51 to 125 watts of power.
From your brief diagnoses it looks to be a bad Power Supply.
barely enough to light the green LED light on the motherboard.
Not enough power to even spin fans, much less turn the Processor on.
Power Supply checks out?
Perform a visual check of the Electrolytic Capacitors on the motherboard. Look CLOSE, and you may need a light, and magnifying glass.http://www.capacitorlab.com/visible-failures/index.htm
Capacitors on the motherboard are used as Filters, and Voltage Regulators.
The one's used as voltage regulators, are in the motherboard voltage regulator circuit.
Some of the one's used in the motherboard voltage regulator circuit, regulate voltage for the Processor.
A Processor MUST have a steady, 'clean', supply of Voltage, and it MUST be kept within a very 'tight' tolerance range. Cannot be too much, or too little, or BIOS will not turn the Processor on.
(Or if on, will not keep it on)
That's an old motherboard. Could be bad capacitors, but I'm more willing to bet on a bad Power Supply.
For additional questions please post in a Comment.