If it worked, it works.
Now when it does not work does the power light come on?
If yes when it works, and no when it does not, power supply.
This can be the on button, or the DC converter, a power board within.
When the backlight goes out, no image, but the power light works, and shining a flashlight on the screen, the image is there, just not lit.
For that disassemble the case, take apart the screen, and replace the back light tube, or, as they are high voltage, they have an inverter, which I think changes DC to AC, a small board that is near the back light tube. Inverters go bad all at once, back light tubes like a florescent they die from the ends. Often the screen turn pink at the edges.
As you have an Emachine, there is also a video card at that end, so if the monitor does not work, try another known to be good, if it does not work, computer video card.
A while back there was a batch of bad capasitors, in everything. They swell, the tops dome, and they leak, they are on the image board.
Two boards in the back of a monitor, image and power, and one small one near the backlight, invertor. the video board on the computer is where the monitor cord plugs in.
I have a ViewSonic VX2235WM-3 that works perfect for fifteen minutes, then shuts down. Turned back on it works perfect for seven minutes, shuts down, then again, three minutes, one and a half, but otherwise a great monitor.
I replaced the capasitors, but cannot figure out what is shuting it down, the picture is perfect. All ideas welcome.