Candela is a pretty poor indication of light output as it generally given for a certain angle. This means LED's advertised with a high number generally have a narrow viewing angle - not good for backlighting.
CCFL's are still used because they provide a nice even light, which can easily couple to the lightguide (the polycarbonate/acrylic sheet that provides a planar light source). In order to replace it with LED's you would need a thin strip of them, spaced close together, butted up against the light guide. As these are "point" sources, you will have what are called "hot spots" where each LED is. LED backlights usually cover the first few millimeters of the lightguide with reflective tape to both hide the hotspots, and to prevent light escaping.
All in all, I do not think you will achieve satsfactory results when compared to the original CCFL backlight. However, if it is just experimenting, learning, or tinkering then by all means give it a go! Perhaps you could buy a strip of white LED's (a 12V strip to make it easier) with 144 LED's per metre. Cut this to length, power it with 12V and see how bright it is.
Say each LED is spaced 100/144 = 7mm apart. And you have a 12" 4:3 monitor - horizontal 24.4cm. 244 /7 = 34 LEDs. Each strip of 3 LED's is powered by 12V @ 30mA. 34/3 = 11 groups. So total power consumption = 11 * 12v * 0.03 = 3.96W. So, if the original screen had a 4-5W ccfl tube, then this arrangement would provide similar light output (LEDs aren't more efficient than CCFL, but comparable).
Google "edge lit display" as this shows how LED backlights work.