Sounds to me like high voltage shutdown.
But my monitor is totally dead!:
Then you probably don't need just a cap kit - although now is as good as any to install one. Search out information on your specific monitor, this will help you repair it. Check the fuses on the chassis - usually failure of one of these is the result of some other, more serious failure elsewhere. You probably have a shorted semiconductor, blown flyback, or something else. See listing of incredibly common monitor failures, in a post below.
What's this B+ I keep hearing about?:
B+ is the name given to the main power supply voltage in a monitor. It's name goes way back to battery operated radios, and the origin isn't important here - but remember that it's the main DC power supply voltage. It's exact voltage varies from monitor to monitor - you'll have to check the manual for your monitor to find out what it should be, but it's usually around 120v. For the Sanyo 20EZ, it's 108v. For the Electrohome G07, it's 120v. For the WG6100, it's 180v. This voltage is adjustable on many monitors, but not on others (WG4900, for one).
So... how does this B+ supply work, anyway?:
Glad you asked (even though I know you didn't). For a usual color raster monitor: Isolated AC enters the monitor chassis from the isolation transformer. This is 120vAC (100vAC for the Sanyo). It goes through the main chassis fuse, and occasionally a line filter. From there, it gets rectified by four big diodes, and turned into DC. This DC is then gets filtered by a big capacitor (usually 680uf at 200v or similar, it's the biggest one on the chassis). After that, it usually goes through a fuse, then into a transistor based circuit containing the voltage regulator transistor and a large ceramic resistor. At the output of this circuit, there is usually a marked test point - or you can just test at the output side of that resistor.
And I test it... how?:
Set your meter to DC volts. Put the black lead on the metal frame of the chassis, and the red lead to the B+ test point for your monitor. This test point may be a labelled point on the board, or it may be one side of the large ceramic resistor - check your monitor manual. If your monitor has an adjustable B+, dial it in using the control. It's important that the B+ be set correctly. Running it too high will result in a picture that's too large, and could cause the monitor to go into shutdown to prevent the HV from going high enough to generate X-rays through the picture tube. Too low can cause a small picture, waves of distortion in the screen, or image instability.