Suggestion is that you see if the problem is the Power On switch, or the Power Supply.
Before you begin;
Check the power coming to the computer. Make sure the power cord for the power supply, is plugged into a working receptacle.
Point in case.
I have now run into three surge protectors where just One receptacle, in that surge protector was bad.
"Hmmm, surge protector power on light is on.
Monitors, printer, and router are plugged into the surge protector, and they are receiving power. Surge protector must be good."
Check THE receptacle that the computer is plugged into. One way is to use a table lamp, or similar device, and plug it into THAT receptacle.
The method to check whether the problem is the Power On switch, or the Power Supply, is to use a jumper on the Soft Power On.
Using the jumper the Power Supply comes on, you have a bad Power On switch.
Using the jumper the Power Supply does Not come on, you have a bad Power Supply.
The eMachines eTower 677ir desktop computer, uses a TriGem Anaheim-3 motherboard,http://www.elhvb.com/mboards/TriGem/profile/anaheim-3/Ana3_304176.htm
You will be dealing with the 20-pin ATX main power cable connector.
Plugs into the white female 20-pin connector on the motherboard, next to the ram memory slots.
[Shown in the above link photo.
You can enlarge the photo of the motherboard, if you wish for more clarity.
Right-click on the photo of the motherboard.
In the drop down list Left-click on - Save Image As
In the small window that comes up, look down at the heading - File name:
To the right of the heading File name: is a box with
304176-360 in it.
Put your mouse cursor right after the 0 in 304176-360
Left-click twice. Type - TriGem Anaheim-3
Go below, and left-click on Save.
This should go to your My Pictures folder.
I believe 304176-360 TriGem Anaheim-3 will be easier to find than just 304176-360.
Double-click on the file name.
In the window go to the bottom, and left-click on the Zoom In icon. Looks like a magnifying glass with a plus sign in it. ( + ]
This is what a 20-pin ATX main power cable, and it's respective connector looks like,http://www.playtool.com/pages/psuconnectors/connectors.html#atxmain20
Viewing the photo to the far Right you will see a wire with Green insulation on it.
This is the Soft Power On wire.
ANY Black wire you see is a Ground wire.
A jumper wire is used to jump across from the Soft Power On wire, to ANY Ground wire.
The connection is a BRIEF one.
It is a Momentary Contact.
(The Power On switch is a Momentary Contact Switch)
You touch the jumper wire for no more than 2 seconds.
Viewing the photo to the far right, you are viewing the back of the connector.
The back of the connector is where the wires go in.
This is where the jumper wire goes.
One end of the jumper wire, will go down into the socket hole that has the Green wire, and the other end will go down into a socket hole with a Black wire.
(ANY Black wire. They are all Ground wires)
I use a jumper wire made from a wire, such as is used on the Power Supply power cable wires.
Same gauge (Size), and has insulation on it.
The jumper wire is approximately 3 inches long, and is bent into a U shape.
Each end of the wire has approximately 1/2 inch of insulation removed.
The bare wire ends are then twisted into a point.
The bare end of the jumper wire has to go pretty far down into the socket hole, in order to make a connection.
It goes down into the socket hole right next to the wire.
At the end of the wires that go down into the 20-pin connector, is a metal terminal. (Socket style)
The bare end of the jumper wire Must touch that metal terminal.
My method is to have the computer unplugged from power.
Insert one bare end of the jumper wire down into the Green wire socket hole. (Soft Power On)
Make Sure the bare end of the jumper wire is contacting the metal terminal.
I then plug the computer into power, and insert the other end down into ANY Black wire socket hole.
It is just a brief touch. No more than 2 seconds.
You may wish to use a glove on the hand that holds the jumper wire.
There Will be a Spark.
The Voltage is 5 Volts DC for the Soft Power On.
Two C cell flashlight batteries produce 3 Volts DC.
It isn't a real safety hazard as you can see, but I wanted you to be forewarned about the spark in advance, so you don't freak out.
If you jump the Soft Power On, and the Power Supply comes on, you have a bad Power On switch.
If you jump the Soft Power On, and the Power Supply does Not come on, you have a bad Power Supply.
(Make Sure the bare ends of the jumper wire, Touch the metal terminals, down in the 20-pin ATX main power cable connector)
The Power On switch is located inside the plastic Power On button.
This is an example of a Power On switch that I have found fits many computers,http://www.directron.com/atxswitch.html
For any questions you may have regarding your problem, please post in a Comment.
(Believe upper right of your page)