Why I'm I having Amber light and refuse to come up?

I had an OptiPlex GX620 with the same problem. The problem was bad capacitors on the motherboard. Pop open the case (Optiplex 360 MT Side Panel Replacement) and look around, see if you can find any capacitors (they look like little cans) that have a bulging top or are leaking fluids out of the top or bottom. If you are able to find any, you will have to buy replacement capacitors with the same specs and desolder and solder in the new ones. It is a difficult repair, but I did it as a complete newbie and my computer works fine now (albeit slow). It was difficult, but the satisfaction of that thing booting up from the dead made it all worth it. You will need a soldering iron, new capacitors, and idealy, a solder sucker or desoldering braid. Here is a guide and some tools you will need. Cómo utilizar una bomba desoldadora

Soldering Iron 60w Hakko 503F

You can find the replacement capacitors on eBay. Just type the info on the capacitor into eBay. You can go higher on the voltage, but not lower, however, the µF must remain the same. I've included pictures of what capacitors should and shouldn't look like.

In the pictures I circled the bad ones in red and the good ones in green. This should help you identify the bad ones to replace. There are some good tutorials on YouTube that can help you do the replacement if you need any help.

Good luck!