Well, the suspect parts are (in no particular order) the output transistor (TR 11), the HV diodes (EHT) and the filament regulator (TR7, if there's no glow on the filament, but it might be ok and just hard to see -- but easy to check that filament pin with a voltmeter and see). Obviously with no filamament it won't work, and that could either be the supply, or the crt -- check that first with voltmeter on the supply and ohmmeter across the filament. I see they link to waveforms, if you've got that data too, check the collector of the horizontal output transistor for the right waveform. In general, the thing turns on and pulls to ground, then off and the collector "flies back" (well above supply voltage) due to stored energy in the flyback transformer and yoke (note they are in parallel for AC). I note there's a diode off the transformer used to make power for other things in there....that's suspect too. A lot of those failed "real leaky" and that would eat enough power to make other things not work.
In these lower voltage monitor circuits failures of the flybacks (and yokes) are comparatively rare compared to the old days of 35kv color tvs with no volt multiplier off the flyback.
The diodes can be a little hard to check as the HV ones are usually really a bunch of lv diodes in series in that package, and it may take tens of volts to turn one on forward, and tens of volts going the other way to expose any serious leakage. Note that they are using the flyback system to generate some of the on board voltages -- that's typical, but it makes things a lot harder to troubleshoot as "everything affects everything else". At the shop, we rigged up a medium voltage (say 48v) power supply and a 10k resistor to test these diodes in a sort of "in circuit" type of test, as the regular diode checker on most meters is useless for a diode that's really 30 in series in there.
I'd forgo replacing all the electrolytics unless they are bulged, got real hot (see pcb for burning) or test bad and you see a lot of ripple across one. They don't fail as much as they used to.
Usually things would sorta half-work even if they were bad -- you'd have something on screen to go by for further troubleshooting.