The monitor will turn on but the screen is very dark and won't lighten up

The problem is in one of the inverter transformers or one of the backlights are defective, unfortuneately this is a job for a tecnician.

fixing a LCD monitor require you to have some basic electronic know how.. changing the backlight won't be easy as you need to dismantle the whole LCD right to the screen..
But if the display only lasted for few minutes and then the whole screen turn dark, this is due to bad component on the board.. most probably capacitor...

u will get options with buttons on your monitor . .increase the brightness and decrease contrast

Use screen adjustment to lighten, if you have done that try it with another PC,

If that works either your vid card (If you have one) or the mobo drivers need updating.

Use brighten controls on monitor to lighten

Try holding CTRL down and pressing F6 to lighten and F5 to darken screen...

Open the monitor menu and turn the brightness up.

This IS an inverter issue. You need a new inverter. Open the LCD and find the inverter model number and search Ebay.
-CharlyV

Hi, This might also work for you, http://www.fixya.com/support/t162607-dim_compaq_s510_crt_colored_monitor However, this involves opening the monitor so not unless you're comfortable working with tools and open units, I would recommend that you ask the services of a qualified professional. Good luck and kind regards.