Check the power cord, or try using another to see if the monitor turns ON.
It should have at least one LED, or you may be able to hear some noise when the unit is ON.
If your monitor takes power from an outlet in the back of the PC power supply (not very common in new systems, but there are, still, many computers with this type of configuration); you should check for proper power in this outlet.
If the problem is inside the monitor you should take it to a technician to fix it. Even if the problem is the fuse inside the monitor (a very common problem) you should not try to fix it yourself; extremely high voltage is present inside the monitor for quite time after disconnecting the power cord (how much time? It depends on the monitor and the discharge circuits it has built-in).
Regards,
_________________
Jose P. Mir
jpm@jpmir.net