Let's diagnose together with the info you have provided.
1) Computer constantly rebooted.
You reformatted using Windows XP. (Fresh installation)
2) Computer powered up, left on all night. Rebooting resulted in Windows will not start again.
Bad Power Supply.
Weak Voltage power rail.
Lights may light, and fans may spin, (Or spin a few times, and stop), but the Processor isn't getting enough power to turn on.
A) ALL the lights use less than 1 Watt of power
B) EACH fan uses 2 to 3 Watts
C) A typical Processor can use 51 to 125 Watts. Depends on what Processor it is. (In this case the power usage is lower than my standard reply)
The Compaq Presario 5410us desktop computer, comes with an Intel Celeron that operates at 1.3GHz (1300MHz), has a Front Side Bus of 100MegaHertz. (100MHz FSB), and fits in a Socket 370 processor socket.
Sources:
HP Support > Compaq Presario 5410us > Product Specifications,
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00009504&tmp_task=prodinfoCategory&lc=en&dlc=en&cc=us&lang=en&product=93299
List of Intel Celeron Microprocessors > Tualatin-256 Core (130nm architecture)
http://en.wikipedia.org/wiki/List_of_Intel_Celeron_microprocessors#.22Tualatin-256.22_.28130_nm.29
Socket 370 processor socket,
http://en.wikipedia.org/wiki/Socket_370
The Intel Celeron sSpec number SL5VR processor can use up to 33.4 Watts.
Why did the computer boot up, and now fall to it's knees?
Electrolytic Capacitors inside the Power Supply were failing, and now have failed.
Primer:
Electrolytic Capacitors used inside an SMPS (Switched Mode Power Supply), are used as Filters.
They filter the incoming AC electricity from your residence, or business, and the outgoing DC electricity produced by the Power Supply.
They are used in the Input Stage, and the Output Stage of an SMPS.
http://en.wikipedia.org/wiki/Switched-mode_power_supply
(Left-click on the photo to the upper right, to enlarge. You can enlarge twice)
Electrolytic Capacitor:
The type of Electrolytic Capacitor used in a Compaq Presario 5410us Power Supply (SMPS), are Aluminum Radial Electrolytic Capacitors.
Basic Construction;
The case is ssentially a small aluminum can case, that resembles a pop can with the top, and bottom cut out.
Inside are three strips.
1) One strip is aluminum foil metal. This strip is the Conducting strip. The Positive lead is connected to this strip.
2) One strip is aluminum foil metal, but has a non-conducting medium applied to it.
This strip is the Non-Conducting strip, and has the Negative lead connected to it.
3) The last strip is a paper-like material, and is soaked with Electrolytic paste.
The paper-like strip is placed in-between the Conducting, and Non-Conducting strip, and all three strips are rolled up tightly together, then placed inside the aluminum can case.
A the top of the can case is a seal, and also at the bottom.
The top seal is a flat thin disk (Aluminum), and has a shape etched part way into it.
The bottom seal is a flat disk composed of synthetic rubber, and the two leads protrude through it. (Positive and Negative lead)
When an Electrolytic Capacitor begins to fail the paste develops a gas inside. (Hydrogen Gas)
(Or the paste simply dries up. Read on)
The gas compromises one, or both seals, and the paste is pushed out. (Oozes out)
So much paste loss, and the capacitor operates at a weakened state.
Too much paste loss, and the capacitor fails.
(To regress;
A capacitor slowly builds up a charge, then releases it all at once.
You can 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)
Closer look at Electrolytic Capacitors, (Aluminum. Aluminum foli is used inside), and outward visual signs of failure. In this example they are being used on a motherboard,
http://www.capacitorlab.com/visible-failures/index.htm
There are occasions that the paste dries up inside, and no outward visual signs of failure are present.
DO NOT open up a Power Supply, and attempt to repair it!
If there are Electrolytic Capacitors that are still good, they can release their charge to you!
[If your finger/s touch the terminals on the bottom of a capacitor, the charge can be released to you!
If your finger/s touch a circuit that one, or more capacitors are in, the charge can be released to you! }
The shock can be Bad to FATAL.
(Especially the 'caps' used in the Input Stage. Viewing the Wikipedia SMPS link photo, the Input Stage 'caps' are designated by the letter A. These puppies hold a LOT of Voltage! ]
A tech will use the proper method of discharging the caps, before working on the electronic device.
Do you have a KNOWN to be good, Compatible power supply, to use for a test unit?
(Compatible:
Must have the required amount, and type, of power cables needed. Must have at least the same amount of Wattage.
More Wattage is just fine. A computer only uses the power it needs, and NO more)
Or you can test the voltage power rails.
(Since there was no indication of power provided by your statement, testing the power supply is really futile, IMHO. But you may want to reserve this information for future diagnoses )
The SMPS used in that Compaq computer, puts out three main Voltages.
1) 3.3 Volts (Orange insulated wires)
2) 5 Volts (Red wires)
3) 12 Volts (Yellow wires)
Specifically you need to check the 12 Volt power rail.
11 to 13 Volts is fine.
Less than 11 Volts requires replacing the Power Supply.
You can use an economical multimeter, or an economical power supply tester. Nothing expensive, or fancy needed for this test.
An economical multimeter can be purchased for around $5 to $12.
(Many stores carry them. An auto parts store is one example)
This is one example of an economical power supply tester,
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=5250576&CatId=5471
The Positive (Red) prove lead is connected to the voltage power wire to be tested.
The Negative (Black) probe lead is connected to ANY Ground wire.
(ALL Black wires are Ground)
What causes Power Supply failure?
1) Low quality hardware components are used inside.
A) Too small a gauge of wiring is used
B) Low quality Electrolytic Capacitors
C) Low quality Rectifier Bridge
D) Low qaulity MOSFET's
To name a few.
2) The computer is dirty inside, as well as inside the Power Supply.
The Power Supply has two cooling components used for it's cooling system.
A) The Fan
B) Heatsink's used inside.
[Typical construction of Heatsink is a flat plate of metal with tall, thin fins protruding from it.
The metal plate absorbs heat from whatever object it is placed against, and the fins absorb the heat from the plate, where they radiate the heat away.
If a fan is used in conjunction with a Heatsink, (Such as a Power Supply, or Processor, for example), the air flow helps to carry the heat away from the fins ]
Once the cooling components for a Power Supply are coated with 'Gunk', the cooling capacity drops tremendously.
Heat = Wasted Energy
The more heat, the more the Power Supply tries to keep up with the call for power.
Eventually the components inside the Power Supply break down, and fail, and the Power Supply fails.
(I have found that usually the Electrolytic Capacitors are the first to go. They are the weakest link)
Have any questions please post in a Comment. (Believe upper right of your page)
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