For your power on LED, it must be polarity that is inversed. Try the other way it should solve that.
Let's examine the possible cause of a computer that boots but doesn't either post nor beeps, and won't ever load any OS:
- RAM. It can be misplaced, or loose. A computer won't beep nor post at all if no compatible/working memory is detected. A defect is also possible. Try swapping slots, or using only one stick at a time in every sockets, try them all, then try swapping with other brand of memory sticks. If you can't post you won't be able to test these with softwares so you have to rectify that.
- Harddisk/Optical drives. Disconnect every power cable from any drives. Sometimes a drive failure prevent from booting by have freezing, crashes, or extremely long bootup time (could take 2-5-30 minutes even hours sometimes when it happens). By disconnecting them you remove that from the equation.
- CPU. It can be bad seated, the cooler on it might not cool the cpu enough nor exercise enough pressure on the cpu making protections preventing it from power on. Try reseating all those and reapply thermal paste accordingly to manufacturer's suggested quantity of thermal paste. Usually about drop is plenty and apply it evenly. If you don't have thermal paste at hand, do this last, and then you WILL have to get some thermal paste before doing it.
- Power supply. This one is easy: try another one, a better unit if possible. A defect power supply can do every and any errors possible. A computer that power up when it is plugged in AC means a cheap power supply is being used. Every quality power supply doesn't act like that. I remember only cheap ones doing this. If not that, a short-circuit between some lines could make it power on when plugged. We use that trick when building a computer on a table. But some wires may be damaged et short-circuit with a ground. Check the cables. Again a cheap power supply has cheaper cables and no internal protections whatsoever so it could be it. You have to remove that from the equation or you will ever wonder.
- Motherboard. A bad/corrupted BIOS can do whatever glitch is possible. An incompatibily between the motherboard with its peripherals: RAM, Graphic Card revision or Cpu revision might imply a BIOS flash to make it compatible. Too bad you can't flash the BIOS when the computer doesn't post. So the only thing to do now for this type of glitch is to switch between computer parts. Switch between RAM first as it is the most common BIOS incompatibility, then the graphic card as it's simple to change it, and at last, the cpu. A motherboard defect might be possible though it's the last thing you know when you have tested everything else.
Please we need to know:
- Is it making any beeps at bootup and if so how many short and long beeps. These are codes used to determine what's the problem.
- What is your rig exactly: motherboard, cpu, graphic card, ram and power supply you are using. This is the second most important question as we will know if compatibility is an issue.
Great details on these would be welcome to resolve that issue.