My monitor wont turn on - LG W1934S-BN 19" Monitor

Once you have confirmed that the monitor is faulty after a test with another monitor of the monitor on another PC, the total loss of power can be due to failure of the power supply in the monitor. This is a switch mode pwer supply and in most cases the driver or the SM oscillator can fail. Attempt to probe only if you are equipped and aware of the SMPS basics.
Please check this link for some tips:

http://www.fixya.com/support/r5826301-working_switch_mode_power_supplies

I assume that your computer is actually turning on (power supply fan is running and CPU fan is running). If this is the case, then do this:
If the monitor is on, there should be a green or blue light on the front or the top to indicate it's getting a signal from the computer. If the light is amber, it means the monitor is on, but there is no signal.
If there is no light, test with a second monitor. If the second monitor works, then your monitor is dead. It needs to be repaired or replaced.
Assuming that the monitor has a light on it (probably amber) then you need to open the computer and disconnect everything but the CPU, video, and memory. Now try to turn it on. If it does not turn on, but all the fans are running, then the culprit is the CPU or the memory or the motherboard. In rare instances, it's the power supply.
If with all this stuff disconnected, you get video, then the problem lies with one of the devices you disconnected. The most common is the CD/DVD.

Test all leads that attach to your hard drive including electrical extensions,IDE,SATA

the leads from your ((motherboard to your hard drive)) make sure they have a secure connection and are not faulty or just replace them they might be faulty make sure all leads that are attached to your drives dvd\cd 3 1/2 inch floppy have secure connections and are not faulty even the electical extensions

even something as small as an electrical fan and its lead can cause this problem or just replace them they could be faulty a computer needs all electrical power and data to continue through every working device and to have an end so any faulty leads will end up with a computer error

make sure your graphics card is securely seated with no dust built up or in the socket

hope this helps you