In general, it's hard to perform reliable in-circuit testing of caps with ordinary instruments (eg, the trusty multimeter) because so many other circuit elements could present sneak current paths and confound the measurement. Fortunately, many failures are sufficiently dramatic that you can sometimes identify failed caps with a visual inspection. Aluminum electrolytics will exhibit bulging and/or outright leakage of electrolyte, for example. Tantalum caps rarely exhibit any visible signs of failure (or they explode with a bang), but almost always fail in the shorted state (easily detected with a standard ohmmeter). A joke among techs is that a shorted tantalum cap is a room-temperature superconductor.
Non-electrolytics can fail either open or shorted/leaky. Shorts are easy to find, opens not so much. A high-impedance analog ohmmeter turns out to be a better choice than most digital multimeters as a substitute for a capacitor tester. With the capacitor out of circuit and your ohmmeter set to its highest-resistance setting (megohms or greater), test for continuity (and verify lack of same), and then reverse the ohmmeter leads as fast as you can. The meter will initially indicate a low resistance, and then should climb toward infinity as the capacitor charges.
For small-value caps, you aren't going to be able to flip the leads fast enough. Without a capacitance tester, there's no easy way to test such caps other than indirectly, through substitution with a known-good one. However, in your case, an open-circuited small-value cap is not particularly likely to cause the symptoms you describe, so devising a test for this situation isn't too high on your priority list. After doing a careful visual inspection and reheating solder joints of the usual suspects, I'd test all of the semiconductors (starting with the high-power ones), and then the switching-supply transformer and flyback. These usually fail in a sufficiently dramatic way that a standard multimeter will reveal it. As with capacitors, it may be necessary to isolate the component under test to avoid false readings caused by other parts of the circuit connected to the device under test.
Another test you can do, and should do if you haven't already, is to see if the power supply is at least ok up to the switcher. You need to exercise caution, however, because the test requires you to probe a hot circuit. Connect your voltmeter across the main filter capacitors (C35/C36) or across the bleeder resistor (R41). For models made for the US market, the voltage will be around 160-170V. If you measure a significantly different voltage, suspect a problem in that area of the circuit. Conversely, if the voltage is ok up to that point, you can move on to checking other circuit bits.
