to read a capacitor you need a capacitance meter otherwise you will not get an accurate reading
normally if i get a monitor fault i start be using a multimeter to prove the mains voltage is correct and present,being in the u.s you would be looking at around 120vac
if thats o.k then the next thing to look at is if the screen flashes when you switch it off,the screen volts on the flyback transformer has any effect on the picture at all when adjusted or if there is a orange glow from the tube neck near the neck card-5 minute job to do the lot.
if none of that can be proved i then look at the solder side of the chassis to check for bad solder connections
after that i check for any obvious component that have fried or in the case of an electrolitic capacitor bulged
after these checks you are then entering the realms of test point checks,whereby you would make voltage checks at various points with the aid of a schematic diagram
also worth listening to see if the chassis is trying to start,this will be either a ticking noise or a whistle-normally this will point towards a problem in the power supply circuit or the deflection circuit(horizontal output transistor being a very common problem)
worth noting that many monitors with a failure in the vertical frame circuit will refuse to start
other checks of course are the chassis fuse and visual inspection of the flyback transformer for cracks or damage including signs of arcing
monitors can be real pigs to fix,i have worked in the arcade industry for 22 years and have quite some knowledge of monitors(not the same league as ken,rick or qrz though)-i get some real problems from time to time(like the neotec 2702 i am working on now)
best of luck