Xeniczone,
The symptoms you describe are the same for a monitor that does not have a signal from a computer. Energy save features turn off a monitor that does not need to be on.
So, the fact that you hear a startup chime leads me to belive you at least have a functioning motherboard. The fact that the computer monitor does not stay on indicated that there is nothing waking up. A PRAM battery may be needed but use the following test to see if other components will respond.
Check to see if you have RAM chips installed, if you have a hard drive. Har the thing been stripped of necessary parts?
Hit the CD eject key and see if the drawer will open and let you put in a CD. If you have a system install CD, turn on the computer, insert the CD, hit the reset button (triangle shaped symbol on a small button by the USB port on the right side down low), immediately hold down the 'C' key on the keyboard and see if it will wake up and recognize the CD (or hard drive, for that matter).
If you do not have an install CD, just play around with turning the computer on and resetting the power switch without turning off the power at the AC source. This will get around a dead PRAM battery for testing purposes.
Jim