I would take the PC nad the monitor to the repair shop and have them find out if the PC is out back together correctly by trying with another monitor, if it works with another monitor, then you will have to take apart the monitor to inspect the inside for bad components.
If you are going to DIY and have proper tools and know safety precaution then please read on:
Most common failures in the LCD monitors are bad capacitors (bulging top/seal or leaking) in the power supply, blown fuses; poor solder joints, failed inverter circuits (blown fuse, shorted transistors, shorted/open transformers), bad lamps (poor solder connections or worn out lamps). You will need to open it up and inspect the inside, see example of failed monitors to get some ideas what to look for: http://s807.photobucket.com/home/budm/allalbums
Post back what you see inside so we can guide you further and it will help out other people in the future also.
http://en.wikipedia.org/wiki/Capacitor_plague
http://www.badcaps.net