Replacing capacitors in a power supply circuit
If you want to test capacitors fully, you will need what is called an ESR meter(Equivalent series resistance) 

Electrolytics have an ESR which increases through general use (age and heat are main factors). 

SMPS (Switch-mode power supplies) are pretty sensitive to ESR. The ripple voltage on the output is calculated as \$V_{ripple} = I\times ESR\$. This means that as the ESR of your caps increases so does the amount of voltage ripple. I can't say with certainty the problems cause by ripple voltage so I've included an extract from Wikipedia.

Effects of ripple

1. Ripple is undesirable in many electronic applications for a variety of reasons:
The ripple frequency and its harmonics are within the audio band and will therefore be audible on equipment such as radio receivers, equipment for playing recordings and professional studio equipment.  

2. The ripple frequency is within television video bandwidth. Analogue TV receivers will exhibit a pattern of moving wavy lines if too much ripple is present. 

3. The presence of ripple can reduce the resolution of electronic test and measurement instruments. On an oscilloscope it will manifest itself as a visible pattern on screen.  

4. Within digital circuits, it reduces the threshold, as does any form of supply rail noise, at which logic circuits give incorrect outputs and data is corrupted.  

5. High-amplitude ripple currents shorten the life of electrolytic capacitors.

Now to answer your actual question. As long as the capacitance and voltage rating match that of your current capacitors then that's all you need. Personally I'd recommend Panasonic capacitors, every time I change an aluminium electrolytic I always change it for a Panasonic capacitor.

The backlight of your monitor shouldn't make any difference to the capacitors you need on your power supply.