The most likeley thing is that the PC is displaying at a resolution or frequency not supported by the monitor.
When you say it turns black after boot do you mean after it finishes post (the basic tests at the very start of the boot process)?
If it beeps very soon after the monitor dies shortly after post then it might be giving you an error about the battery on the motherboard asking for you to press a key to confirm the message. If this occurs then sometimes the display is out of range for the monitor to display, if this is the case (and the PC is a Dell like the monitor) press F1 after the beep and your PC should continue to boot.
Also try going into the BIOS setup during the boot phase (usually F2 on a Dell) and see if the monitor behaves the same or if it stays on for longer.