Hi there,
U1 looks like a fully integrated switcher ( like a TOPSwitch from PI). Those should be easy to come by. I would desolder it and check for a short or low-resistance path between the output and other terminals. That is the most likely suspect.
Als check the clamping circuit across the primary (D6, D7, C28). With U1 desoldered, carefully check the DC bus voltage across C3. That should be around 285VDC. Carefull, it is lethal!
You can also check wether the control voltage for U1 is present across C5. That should be around 12V. It may be that the feed-back terminal on U1 is blown as well, so U2 may still have survived. You can also check this with U1 desoldered.
If all of that check out, you can safely replace U1 and give the supply another go. I recommend using a lght bulb in series with the live wire as a current limiter. When you power on the bulb will flash momentarily as a result of the inrush caused by C3. After that is should go out almost completely and shine dim when you load the supply. Judging from the size supply, a 20W-40W bulb should suffice.
Happy repairing.