It’s difficult to pinpoint the exact reason without seeing your board and soldering quality. Here is a reference image of the soldered board:
http://rayshobby.net/wordpress/wp-content/uploads/2013/04/svc142_build_back.jpg
There are a few tests you can start with:
– measure the resistance between VIN and GND, and also VCC and GND. If any of them is small (less than kilo-ohm level), there is probably a short somewhere.
– since your IC1 is burned, you should also check the related elements, particularly D1, D2, D3, and see if they have been damaged in any way. To check these diodes, use a multimeter to measure the forward drop voltage. D1 and D3 should have 0.5-0.7V, and D2 should have around 0.2V. If the forward drop voltage is shown to be close to 0, the diode is burned and needs to be replaced.
– Try to power the circuit board through USB and measure the voltage between VIN and GND, and also VCC and GND, see if they are roughly 5V and 3.3V respectively.
Regarding the three 220uF capacitors, I apologize for the issue. Just to make sure: since the 220uF and 10uF capacitors are very similar in appearance, did you check the label on the capacitor body to see they are actually all 220uF?
Thanks for pointing out the missing Rain Sensor step. Will add that to the instructions later.