My dell GX620 desktop does not power when ever I plug in the network (RJ 45) cable. Also if the system has boots to desktop, and I plug in the network cable it automatically goes off.

SOURCE: No power to Dell demension 5100 desktop

If there is no activity whatsoever when you press the power button on than you have likely blown the internal power supply fuse. This will need a technician to repair.

SOURCE: Dell Optiplex GX620 PC is failing to power up

You may have a failed motherboard then. Failure of motherboards is usually due to breaking capacitors. A few years ago a capacitor company stole the "recipe" for making capacitors from another company and tried to make their own, unfortunately they did not get the ingredients right and the capacitors started breaking after 2-3 years of use. They sold these capacitors at very cheap prices and a lot of computer companies and power supply makers bought them. This is easy to diagnose. Look for capacitors (caps) (they look like little tiny soda cans) on your motherboard (mobo). They should be perfectly flat on top and not bulged or swelling or leaking anything. Make sure you look at all of them, on DELL's especially look under the cooling fan shroud as well. The dead giveaway is the fact that you are not getting anything after you changed the PSU. There are a few companies that will repair broken capacitor issues. Also if you add a bunch of extra components without upgrading the power supply you can suffer underpowered situations and that can cause internal parts to fail.
To eliminate some other stuff you could remove the memory and disconnect all the power plugs from the drives and then try to start it up. If it does not change the behavior at all (no beeps, no change in flashing lights) then you probably have motherboard issues. Make sure when disconnecting the memory chips (sticks) that you touch the metal on the inside of the case first to discharge static electricity. If it does change the behavior add 1 component or item back at a time to see what you can find out. Post back with what you find. And remember a bad PSU does not mean no power, just not enough to run the computer. Is the PSU that you replaced the same or greater output watts?

SOURCE: Can't boot up Dell 5100 Dimension, amber light flashes

When you mean the amber light, is that the blinking hard drive access light or the power light? Different cases have different colors on it. Mine has blue and green lights.

If you see the boot screen (bios) and then after it goes to boot, does it blink and hang?

This could be a simple operating system issue, hard drive or hardware/motherboard issue. If you could provide more information, that would help.

SOURCE: Adding network drivers to dell optiplex gx620

Just download the drivers here the link http://support.dell.com/support/downloads/driverslist.aspx?c=us&l=en&s=gen&os=WW1&osl=en&catid=&impid&SystemID=PLX_PNT_P4_GX260

SOURCE: I have four dell optiplex gx620 computers. Three

First check your power supply at the outlet. If that is okay, check that the power is turned on at the back of the cpu. If still no power check the power cord. This part should be easy since you have a computer that still works. Just switch the power cords. It does sound odd since all three stopped at the same time. But if they all run off the same circuit you could have a bad fuse or tripped breaker.