1) Make sure the surge protector your computer is plugged into, has power.
Could be the surge protector isn't any good.
Could be that the wall receptacle the surge protector is plugged into, doesn't have power.
2) Make Sure THE receptacle IN the surge protector, that the computer is plugged into, has power.
I have had more than one surge protector in the past, where just THAT receptacle the computer was plugged into, was bad.
"Hmmm, power on LED light of the surge protector is on.
Monitor, printer, and router plugged into the surge protector have power."
If this holds true for you, remove one of the peripheral's power cables out of it's receptacle in the surge protector, and plug into the receptacle the computer is using.
[A monitor, and a printer are two examples of a Peripheral]
Make sure THAT receptacle has power.
3) Bypass the Power On switch, to see if the problem is the Power On switch, or the Power Supply.
If I were to hazard a guess, my hypothesis would lean towards the Power Supply.
Power Supply failure, is one of the leading causes of computer failure.
Causes for Power Supply failure are generally,
A) Computer is dirty inside, as well as the inside of the Power Supply.
Dirt, dust, hair, carpet deodorizer, you name it, is 'inhaled' by the fans of the computer. No matter how good a housekeeper a person is, the above mentioned 'gunk' is going to get inside.
This 'gunk' is drawn through the computer, and drawn into the Power Supply.
[Computer case fans draw air into the computer from the front, or side.
The air is 'exhaled' through the rear of the computer.
The Power Supply fan draws air into the Power Supply, and pushes air out of the Power Supply, towards the rear of the computer.
Computer case fans in the rear of the computer also push air out.
A typical ATX style of Power Supply,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4236686&sku=C13-2507
This 'gunk' coats the cooling components of the computer, and drops the cooling capacity of these components tremendously.
Heat = Wasted Energy
When the cooling components of the Power Supply, (The fan of the Power Supply, and Heatsink's which are used inside), are coated with 'gunk', the Power Supply heats up.
The more heat, the more the Power Supply strains to keep up with the call for power.
Eventually components inside the Power Supply fail, and the Power Supply itself fails.
The inside of the computer, as well as the inside of the Power Supply, should be cleaned on a regular basis as needed.
The computer should be unplugged from power, computer case open, and Anti-Static precautions followed before using the air.
[Q-tips can also be used to help remove a heavy buildup of 'gunk'. The Q-tips are just used to break the 'crust' of the gunk, and the can of compressed air can then remove it]
B) Low quality Power Supply
Low quality components are used inside the Power Supply.
1) Gauge (Size) of wiring is too small.
2) Low quality Electrolytic Capacitors
3) Low quality Rectifier Bridge
4) Low quality MOSFET's
Just to name a few components.
Everex seemed to be a quality manufacturer of pre-built computers, from my research.
They typically used generic Power Supply's that were of average quality.
(Management of the company seems to have been Everex's downfall)
If the Power On switch is bypassed and the Power Supply comes on, the problem is the Power On switch.
[One generic Power On switch that I have found fits many computers,http://www.directron.com/atxswitch.html
If the Power On switch is bypassed, and the Power Supply does NOT come on, the problem is the Power Supply.
The Power On switch is bypassed, using a jumper wire in the ATX main power cable connector.
[Has nothing to do with the Power On switch directly]
I don't know if your model of Everex computer used a 20-pin, or 24-pin ATX main power cable.
Typical 20-pin ATX main power cable,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
Typical 24-pin ATX main power cable,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain24
The Green wire you see present in both ATX main power cables, is the Soft Power On wire.
This is BRIEFLY connected to any Ground wire.
ALL Black wires you see are Ground wires.
The Voltage present is 5 Volts DC.
Two C cell flashlight batteries produce 3 Volts DC.
There is a proper method for doing this procedure, that I would like to outline before you attempt it.
Should you wish to attempt this procedure, please state so in a Comment.
Even with the model number of your Everex desktop computer, I may not be able to give you exact guidance in opening your computer case.
With your patience, and our communicating back, and forth using Comments, I Can guide you in opening the computer case.
[Computer UNPLUGGED from power. Anti-Static precautions followed once the computer case is open]