At this point I would take the diagnoses further. This of course depends on you, and if you feel comfortable with the procedure.

However I would like to back up for a moment, and would like you to check that the computer is indeed getting power.

The next part of the diagnoses is to check the Power On switch, then the Power Supply. It would be embarrassing, to find out there was no power at the surge protector.

Would like you to plug the monitor, or a table lamp into THE receptacle socket of the surge protector, that the computer is plugged into.

I've had an occasion in the past where the surge protector power LED was on, and all other devices that were plugged into the surge protector, were receiving power. (All but the computer)

After going through a diagnoses of bypassing the Power On switch, and then checking the voltage output of the Power Supply, I found that THE receptacle that the computer was plugged into on that surge protector, was bad.

All the other receptacles worked fine.
(Monitor, DSL wireless router, sound system amp, etc)
It's akin to removing a fuel system on car, then finding out it was just out of gas.

Checking to insure that the Power On switch is bad, requires bypassing the Power On switch, using a jumper wire.

If the Power Supply comes on, then the Power On switch was the problem.
If the Power Supply does not come on, then the Power Supply is the problem.

When a computer power supply is plugged into power, there is always a constant 5 Volt standby power in the Power Supply.

This 5 Volt power is used to turn the Power Supply on, when the Power On switch is pressed.

Pressing the Power On button momentarily closes the Soft Power On circuit, and the Power Supply turns on.
(The Power On switch is a Momentary Contact Switch)

The Power On switch is not disturbed. The jumper wire is used on the
20-pin ATX main power cable connector.

This is an example of the above power cable, and connector;

http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20

Viewing the photo on the right, observe the wire with Green insulation, and the three Black wires next to it.

The Green wire is the Soft Power On wire.
The Black wires are Ground wires.
(ANY wire with Black insulation, is a Ground wire)

The jumper wire goes from the green Soft Power On wire, to any black Ground wire.
The connection is momentary. Just like the Power On switch.

The jumper wire is constructed out of a wire that is the gauge, (Thickness) of wires like you see used for the 20-pin ATX main power cable.

It should be an insulated wire. The length is up to you, but I would advise it to be at least 3 inches long.

The insulation of the wire is stripped off on both ends. 1/2 inch of insulation stripped off should suffice. The ends are twisted, then the jumper wire is bent into a U shape.

The wires that go down into the 20-pin main power cable connector, go down into a square socket hole.
At the end of each wire is a metal terminal.

The metal terminal is down in the socket fairly deep, and care should be used to insure that the jumper wire is going down in far enough, to touch the metal terminal.

One method is to have the Power Supply unplugged from power, then insert one end of the wire in the Soft Power On wire socket hole. (Green)
Then the Power Supply is plugged into power, and the other end of the U shaped jumper wire is inserted into a Ground wire socket hole.
(Black)

The wire is just touched momentarily. A 2 second contact should suffice.

There may be a small spark. Hence the insulated wire. You may wish to wear a glove.
I'm stating this procedure using above standard safety precautions.

If upon touching the jumper wire, as outlined above, does not turn on the Power Supply, then you have a bad Power Supply.
If the Power Supply turns on, then you have a bad Power On switch.

Behind that plastic Power On button, is a Power On switch,

http://www.directron.com/atxswitch.html


HP Compaq DV7600 Small Form Factor Desktop PC documentation:

http://h18000.www1.hp.com/products/quickspecs/12253_div/12253_div.HTML

Have you checked the power supply unit of the equipment?
Is it working?
If yes, the next step would be to confirm whether the memory is healthy.
If both the memory and the power supply are working, then the problem may not be too serious, otherwise, you will need to replace and go deeper and check the status of the motherboard and the processor unit.

*Note: All drives should remain disconnected during the testing process