My monitor turn on but there is no display at all, but in but when I replaced it with another monitor it works. I can say that there is no problem with my computer because I check all hardwares.

If one monitor works on your computer, and the other displays nothing at all, then that monitor is bad and needs replaced.

Assuming it doesn't have multiple sources and its not switched to an incorrect one.

Is your monitor a CRT or LCD?
If it's an LCD you might want to have it checked out, even though LCD monitors are fairly inexpensive these days, you may only need the backlight replaced. If the cost to replace the backlight is almost as much as a new monitor your eying then you have a decision to make. Also if you bought the monitor quite a while ago and you chose it for special reasons (Like a $500 View Sonic Pro for photo and video editing) it might be in your best interest to get it repaired no matter what the cost.