1) So you tested the monitor on a working computer? Reason I ask, is that you will be testing the monitor cable also.
If it is a monitor with a detachable monitor cable, suggest you test the cable also.
2) Each graphics (Video) adapter card has it's own specific driver.
The driver should be installed Before, the graphics card is installed.
Otherwise Windows will 'break it's neck', to find a compatible driver, from it's thousands of generic drivers.
Won't do. You will get a driver conflict.
Windows: 'Which driver do I use? These or THESE?"
Kinda' hard to do, since you can't see graphics on the monitor.
I would like to suggest you diagnose the Power Supply to start with. (After checking the monitor cable)
It may seem that the Power Supply is okay, but it could have a weak Voltage power rail.
Enough power to light LED lights, and spin fan's, but not enough power to turn the Processor on.
1) ALL the LED's use less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts.
3) A typical Processor can use 51 to 125 Watts.
(Lower for older Processors)
The eMachines T6528 comes with an AMD Athlon 64 3500+, processor, that fits in a Socket 939 processor socket,
1) eMachines Support > T6528 > Specifications,http://www.emachines.com/support/product_support.html?cat=Desktops&subcat=T%20Series&model=T6528
2) Information on the AMD Athlon 64 3500+,http://en.wikipedia.org/wiki/List_of_AMD_Athlon_64_microprocessors#Athlon_64
Can use up to 67 Watts, or up to 89 Watts. Depends on what Core it is.
(Clawhammer Core, Newcastle Core, Winchester Core, Venice Core, Manchester Core, or San Diego Core)
(Also uses an MSI K8NGM-L motherboard. Below for specifications only,http://www.newegg.com/product/product.aspx?Item=N82E16813130041
A) Not to down eMachines, (I have an old T1090 in my shop that works great), but they are budget computers, and use budget parts.
One being the generic Power Supply that is used.
B) The computer could be dirty inside, as well as inside the Power Supply.
The cooling components for the SMPS, (Switched-Mode Power Supply,) are it's Fan, and Heatsink's used inside.
Once a layer of 'Gunk' covers these cooling components, the cooling capacity drops tremendously.
Heat = Wasted Energy
The more heat, the more the Power Supply strains to keep up with the call for power.
Eventually hardware components inside the Power Supply fail, and the Power Supply is toast.
You can test the Power Supply voltages.
You can use a multimeter if available, or an economical unit can be purchased for around $5 to $12, that will suffice for testing.
You can also use a power supply tester.
Voltages produced by the SMPS used in a T6528 are,
A) 3.3 Volts (DC)
B) 5 Volts (DC)
C) 12 Volts (DC)
Testing should be done on the 12 Volt power rail.
11 to 13 Volts indicates a good Power Supply.
Less than 11 Volts means it's time to replace.
Orange wires are 3.3 Volts
Red wires are 5 Volts
Yellow wires are 12 Volts.
All the color coded Voltage wires, lead back to one individual power rail, for each Voltage produced by the Power Supply.
You can test any Yellow wire to test the 12 Volt power rail.
With a multimeter, the Positive (Red) probe lead connects to the power wire to be tested.
The Negative (Black) lead connects to ANY Ground wire.
ALL Black wires are Ground wires.
They all go back to one central Ground source inside the Power Supply.
[Power Supply unplugged from power before attaching probe leads. After connecting, the power supply is plugged back into power, and the Power On button is pushed ]
(Two C cell flashlight batteries produce 3 Volts DC)