There is no indication of power to the monitor. I

You are infromign that checked VGA and power cables with a substitute monitor. Might be useful to chek your computer actually working with that substitute monitor.
Additionally, in most monitors, when turned on but not connected to the computer's video outlet, you get a message tinicating something like "NO SIGNAL", or in any vay, making you to know that your monitor is not connected.
If disconnected to computer but with power on you only get a black screen, you've got a defective monitor.
I'm not an electronic technician so can't suggest you what parts you should replace to rpair you monitor, so it you don't really have technical experience repairing monitors, you should take it to repair service.

A dead monitor indicates a power supply problem. If unit has an external power supply and you have have substituted it with another known working supply and the unit still does not work, then the problem lies within the monitor's circuits. Yes, it can be repaired, but it might just be cheaper to replace it due to high labor costs.

Make sure your monitor connectors are seated and the monitor is powered. If so, borrow another similar monitor to test your PC. It could easily be your monitor or your video card. With a substitute monitor you should be able to find out quickly.

If the monitor is showing you a "no signal" message, it's almost certainly working fine. There's no video coming in from the computer, and that's likely where the problem is. Try another monitor first. It's possible yours isn't recognizing the input signal, but it's unlikely. I've only seen that happen twice I can remember. Chances are that another monitor will say "no signal" as well. Either the computer isn't starting up, or the video isn't working.

If you hear all the sounds of a normal startup (usually a single beep when the motherboard finishes power-on tests, hard drive activity shown by the front panel indicator, and finally the Windows startup sound through your speakers), then the video circuitry is bad. If the video is integrated onto the motherboard, you can install a replacement video card in an open expansion slot. If you already have a separate video card you can replace it.

If the computer isn't starting, you need to suspect memory, the motherboard, power supply or processor. You might also have a bad hard drive, optical drive or other device connected which is preventing startup. Begin by unplugging everything except the main parts: memory, processor and fan, power supply and (if used) video card. If the system starts up, you can identify the bad part by reconnecting them one at a time until the problem comes back. If the system still doesn't start with the minimum hardware, part substitution is how you'll figure out which is responsible.

It can be frustrating, but you'll get the thing going. Good luck, and thanks for using Fixya!

check the power cable by substituting with the one working,if no power, you have to change the inverter

I presume you mean there is no video? Is it getting power? You will have to check what is faulty, you can do this by seeing if your PC works on another monitor. Or checking your monitor on someone else's PC, If it does doesn't go, then there is your problem... faulty monitor.. If it still does NOT go then it is your PC and possibly your Video Card, this has to be checked in the same way IE: Substitute another card and test, & so on. Else you will have to take it to a reputable repair man/shop and ask for a firm "Quote".

Good day sir/ma'am hi, if you monitor turns black, here are the more common probable reasons;

1. Your PC went to standby the screen saver kicks in, just reset your PC then the monitor will power on again.
2. If not, your PC is not giving you video signal, check to see if another monitor will work, we then know what part is bad, the monitor or the PC.
3. If the monitor is the culprit, then your monitor's back light or inverter board just went bad. you need to replace it.

There are usually two main circuit board on your monitor, the power supply board and the main board, at this point, you need a professional to do the work.
The process is opening the monitor and locate the LCD screen connection to the main board, to check if the contact is snug. we then test. if still nothing happens, Then we go to the power supply board, to check for connection problem, It would help if there are light signs, like blinking, orange, red, green and the likes? Anyway, if the power supply board is not the faulty one, we substitute the main board with a good one and test to see if it will work, test again. If still no respond, we test a new LCD unit, then test, at this point the monitor is working already, if not, we then replace the power supply board. Huh, very expensive, we already have a new monitor. Reminders, these are to be done by a trained personnel. If you attempt to service this, its expensive, so I suggest you let the service shop do this for you to replace only the faulty part.

robyn_e_fox, Here is what I would try to do first if my 12 to 15 month old LCD monitor started doing STRANGE things!! If possible try to substitute a KNOWN GOOD monitor in it's place to make certain that your PC is working properly. If PC is OK then you know or are pretty sure that your LCD could be having an internal problem that a technician will need to diagnose and repair. Before paying for ANY repair you should contact the monitor manufacturer and complain about the short life and PREMATURE FAILURE of this LCD. Check to see if they also have a swap-out program in place. And last but not least check with the store where you originally purchased the LCD on what you should do. Hope this helped. loiue12fix on fixya lmistyrel @aol.com

LED is on that indicates the power supply is working, so most likely you have there problem with inverter/backlight. To see easier how backlight behaves, unplug flat cable from processor board, so display itself won't be powered and light will go through it. Now if you turn on the monitor you will see the screen turns white for some short time and then turns off again. That's because CCFL driver chip turns into protection.
If you won't see any light, check the fuse on inverter and FETs in primary of inverter transformers.
If those are ok, next, you can localize the lamp, causing the problem - disconnect them one by one substituting with 27pf 3kV capacitors (equivalent load) and try turn on again until white light will stay for longer (while the controller is recognizing the signals from VGA input).
Post here the picture of inverter board (from the driver chip side).

With nothing attached to the mother board except 1 stick of RAM in the first slot the power supply and monitor attached, and then  it still turns off ; I would make sure the heat sink was clean Reseat the Cpu and try it again. Now if the same results. I would attempt to substitute a different known good power supply. If that would not work, you are down to substituting a different CPU .