first of all, i recommend having a good multimeter. something digital. I'm not saying go out and buy an $800 fluke or agilent. But spend 30 or 40 bucks and get a half decent one. 500V MINIMUM. something "autoranging" is best (albeit a little more expensive), especially if you don't know much about what you are testing. It'll pay for itself in avoided frustration. if you have a particular store you will shop at that has a website (walmart etc), let me know, and i'll recommend something that's good and available.
secondly, what you are going to want do is remove the monitor and plop it on a nice big bench. a pad or foam in front so you can tip it onto it's front if need be and not scratch it up. bath towel, moving pad, foam, etc.
Third, make yourself some kind of adapter so you can plug the monitor into an outlet easier. You aren't going to want to drag the cabinet over every time you want to check it. nothing fancy. chop off a cord and use some wire nuts or something to get 'er on there. be safe...respect the white/black color coding. you don't want to mix up your live/neutral wires. you'll end up electrocuting yourself.
Fourth, DON'T ELECTROCUTE YOURSELF! this should be #1 but hey, i'm lazy, i just got off work, and i don't want to go back. Don't touch stuff while it's plugged in. Don't touch some stuff while it's NOT. lots of these capacitors hold 50+ volts...some of these capacitors hold 200 volts or more in them and they don't feel particularly nice when you touch them. anything over 40Vdc is considered HIGH VOLTAGE and should be avoided. Voltages greater than 50 V applied across dry unbroken human skin can cause heart fibrillation if they produce electric currents in body tissues that happen to pass through the chest area.
still into fixing it?

it's alot to absorb, but if you think you can tackle it... let's be sure you are really ready.