EMachine T3958 Won't start - Please help

The green LED indicates that the standby voltage is present which is what provides the power so the front button can tell the unit to turn on fully.
At that point, there are 3 possibilities; the power supply has a fault and won't turn on, the systemboard has a fault and prevents the supply from turning on, and/or a connected device is causing a short.
Normal troubleshooting would consist of:
1) Trying another power supply (just set the system on its side and you only need to plug in the two connectors to the systemboard after unplugging all of the suspect supply's wires) If it then works (yeah!), hook the power back to the drives, see it boot, turn it off, then replace the supply inside the chassis.
2) Using the test supply hooked up to the systemboard, remove any add-on cards (modem, video, any USB devices, etc) and unplug the IDE (hard drive cables) from the systemboard. If it then works, put things back, one at a time, to find out which is fried.
3) Reseat the memory and CPU chip and try one last time.
If it is still no go, the systemboard is bad.
If you get to that point, this guy will need new video drivers; but, is a newer board which will let you upgrade further in the future: http://cgi.ebay.com/eMachines-Seabreeze-Motherboard-D845GVSR-103292-102240_W0QQitemZ260328632136QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item3c9ccbaf48&_trksid=p3286.m20.l1116

You need a voltmeter to check the supplies

5vdc & 12vdc are the two easiest becasue they are are the ones which are on the connector which supplies the Hard Drive you have just replaced

Red is 12v Positive Yellow is 5v Positive and the black wire is Neutral

You can remove the main board connector from the power supply to the MB but you need a copy of the Motherboard installation manual to tell you what supplies are on that connector