There are many possible failure modes. The snag with troubleshooting SMPSUs is that if you don't change all the faulty parts, and there are often several, then the next time you switch it on for testing, the ones you replaced fail again. There are ways round this, such as with a lamp limiter, but fixing even a simple little supply like this can be fiddly and annoying, even with experience.
I personally don't suspect the reservoir capacitor or the transformer, as it has not had many power-on hours (caps are usually the first thing to fail in SMPSUs that are on 24/7 though). I can't see the power switching device but that, and the IC that drives it, the startup resistor (if fitted) and current-feedback parts are common causes of random failures.
I'd check for dry joints, check the DC output for shorts (which could be the output rectifier or reservoir) and any obviously vulnerable items such as current feedback resistor, other fusible resistors, startup circuit, output transistor and efficiency diode. If all looks OK I'd energise through a lamp limiter and isolating transformer to make sure there is 340V DC on the input reservoir that is reaching the transistor. OTOH if it's a monolithic IC, I'd pull it, test around it again e.g. up the opto-coupler for domino-effect faults, replace, then repeat from top.
Actually, no. I wouldn't bother, and I have loads of experience fixing SMPSUs. It probably isn't worth the agro.