Bad Power Supply.
Weak Voltage power rail.
I'm going to explain what is wrong, and why.
Power Supply's are rated in Wattage.
The Power Supply used in a Compaq Presario SR2030NX desktop computer, is a 300 Watt unit.
1) ALL the lights use Less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts.
3) A typical Processor uses 51 to 125 watts. Depends on what Processor it is.
The Compaq Presario SR2030NX uses an AMD Athlon 64 X2 3800+, processor,http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00754206&tmp_task=prodinfoCategory&lc=en&dlc=en&cc=us&lang=en&product=3245050
The AMD Athlon 64 X2 3800+ processor can use Up To 89 Watts, (Windsor Core)http://en.wikipedia.org/wiki/List_of_amd_athlon_64_processors#.22Windsor.22_.28F2_.26_F3.2C_90_nm.29
(HP Support lists the Processor as an Athlon 64 (O) 3800+.
The (O) should be an X2)
This means your bad Power Supply has enough power to light lights, and spin fans, but not enough to turn the Processor on.
No Processor running, No computer.
Bad Voltage power rail.
Inside the Power Supply are Electrolytic Capacitors.
Electrolytic Capacitors can break down.
The capacitors are used as Filters.
They filter the incoming AC electricity (Input Stage), and the outgoing DC electricity made by the Power Supply. (Output Stage)http://en.wikipedia.org/wiki/Switched-mode_power_supply
(Observe the photo to the upper right of the page. The photo can be enlarged by left-clicking on it. It can be enlarged twice)
Electrolytic Capacitor simplified construction:
The Electrolytic Capacitors used in the Power Supply, (And on the motherboard), of a Compaq Presario SR2030NX, are Aluminum Electrolytic Capacitors, which are of the Radial design.http://en.wikipedia.org/wiki/Electrolytic_capacitor
Observe the two photos of capacitors, shown at the upper right of the page.
The Electrolytic Capacitor example shown at the bottom, of the bottom photo, is the Radial design.
(Short blue capacitor)
The case of the capacitor is an Aluminum 'can'.
Inside the aluminum can are three strips.
1) One strip is an aluminum foil, and is the Conducting strip.
2) One strip is an aluminum foil, and has a non-conducting medium applied to it.
This is the Non-Conducting strip.
3) The last strip is a paper-like medium, and is soaked with Electrolytic paste.
The paper strip soaked with Electrolytic paste, is placed in-between the Conducting, and Non-Conducting strips, and all three strips are rolled up tightly.
(The Positive lead of the capacitor is attached to the Conducting strip. The Negative lead is attached to the Non-Conducting strip)
When a capacitor breaks down the paste inside develops a gas. (Hydrogen gas)
This gas expands inside the case of the capacitor (Can)
At the bottom of the 'Can' is a seal. It is a synthetic rubber like material, and is shaped like a flat disk.
The top of the 'Can' has a shape etched part way into it.
The shape is commonly an X, or K.
When the gas expands, and develops enough pressure, either the seal at the bottom is compromised, And/Or the etched shape breaks open, to relieve the pressure.
The Electrolytic paste is pushed out.
So much paste loss, and the capacitor operates at a weakened state.
To much paste loss, and the capacitor fails.
A Capacitor as a electronic component that slowly develops a charge, then releases it all at once.
You may compare it to a large swimming pool being filled up by a garden hose, then one wall of the swimming pool is taken down all at once.
This is why the Power Supply worked when you unplugged it for a while, then plugged it back in.
The weakened capacitors paste chemical composition, allowed the capacitor/s to revert back to a working stage once power was removed.
(Power Supply unplugged from power)
When you plugged the Power Supply back into power, the capacitor/s were working again.
Worked with so much paste loss.
Eventually enough paste was pushed out, and the capacitor/s have failed.
What causes Power Supply failure?
1) The inside of the computer is dirty, as well as the inside of the Power Supply.
The cooling components of Power Supply is it's fan, and Heatsink's located inside the Power Supply.
[Refer back to the photo of the open Power Supply, in the SMPS link]
(A Heatsink is a component, that draws heat away from another component.
Typically, a Heatsink is composed of a flat metal plate, that has tall, thin fins protruding from it.
Heat is absorbed into the flat metal plate, whereby it is absorbed into the tall, thin fins.
The fins radiate the heat away.
When a fan is used in conjunction with a Heatsink, the air produced by the fan goes in-between, and around the fins, and helps carry heat away)
When the fan's blades, center hub, and surrounding cage are dirty, and the Heatsink/s are dirty, the cooling capacity drops tremendously.
Again, Heat = Wasted Energy.
The Power Supply tries to keep up with the call for power, and eventually components inside the Power Supply fail.
Electrolytic Capacitors are the weakest link, and typically fail first.
2) The computer manufacturer used a cheap quality Power Supply.
Cheap quality components used inside the Power Supply.
If you wish I can guide you in testing the Power Supply.
You'll need an inexpensive multimeter, or an inexpensive power supply tester.
(One example of an inexpensive power supply tester,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=5250576&CatId=5471
Or if you have a KNOWN to be good, compatible power supply, you can use it for a test unit.
Need help in finding a replacement Power Supply, or information in how to replace it, simply state so in a Comment.