I'd love some education. This certainly looks like a RIFA filtering capacitor to me (just for clarity, the yellow one that says "RIFA"):
Assuming that's an SMPSU, the big RIFA could be part of the start-up chain* although they are more typically low value electrolytics in that position: They are often mounted near hot-running devices and evetually dry out as they don't have a lot of electrolyte to lose.
Maybe someone decided, in this case, to use a non-electrolytic for that application so it wouldn't fail in the way that electrolytics typically do.
* In a typical SMPSU using a high frequency transformer between the mains side and the low voltage side the control IC runs on a separate output on the low voltage output side of the transformer. This is of course impossible, how could the SMPSU ever start if the controller runs on the PSU's own output? The answer is that it receives a brief 'kick' of DC power derived by dropping the rectified mains voltage, typically through several series resistors with the same high value: The capacitor is used to limit the duration of the start-up power feed to just long enough for the control IC and therefore the SMPSU to get up and running: After that, the control IC continues to run on voltage supplied by one of the output windings.
Failure of one of the start-up components - typically one of the series resistors failing open-circuit or the capacitor drying up - is a common cause for an SMPSU to not start when there are no obviously blown up components and the mains input fuse is intact.
Two other tell-tales for this fault condition are:
-The unit ran continually for days / months / years, but wouldn't come back on after a mains power failure. It is possible for the startup components to die while the PSU is already running, and for that to only make itself known when the mains is eventually removed and reinstated, at which point the PSU will not start.
-When investigating this possible fault, be careful to check for stored charge on the large mains side electrolytic capacitors. If mains has been applied but the SMPSU did not start up, then the mains was removed again, the capacitors will very often still be holding a full charge days, week or months after the PSU was last connected to the mains - unless they happen to have very high value discharge resistor connected across them - they sometimes do, but just as often don't. Finding a stored charge on these capacitors is another possible clue that a startup component has failed. If you see stored voltage on them, use a high value resistor held in well insulated pliers to discharge the capacitors before looking further. An analogue multimeter can also be used to do this, because they draw significant current from the circuit under test - with the added bonus that you can see the DC voltage slowly decreasing for as long as you keep the probes on the capacitor.
So - although your PSU hadn't actually failed, this is one possible reason why removing the cap may have stopped it from working: It may be the start-up capacitor.
