Is my board broken by soldering?
It looks like you have soldering paste all over the circuit board. If enough paste bridges a gap between the ceramic resonator and the IC, it can attenuate the oscillator signal to the point where the board won't work.

I use an old tooth brush and Isopropyl alcohol to clean excess soldering paste. As the alcohol evaporates, a lot of moisture forms on the circuit board, so it's important to ensure it's completely dry before you power it up.

Try cleaning the circuit board and see if that fixes the problem.

EDIT:

I would like to show you how much soldering paste it takes to stop a 328P from working. The following image shows the bottom of a perfboard with 0.1" hole spacing. You can see the soldering paste bridging the gap between pins 8, 9, and 10 of a Atmega328P DIP IC. Pin 8 is ground, and pins 9 and 10 are connected to the crystal / capacitors. All three pins are connected together via the paste, and since I forgot to clean the board before "final assembly", it's possible other pins are connected together via the paste.



The circuit board is from a "kitchen clock project", and was taken the day it stopped working. There are no mechanical connections to this circuit board except for the 328P's IC socket. This clock worked for 3 months, then it quit suddenly. I re-booted it once, it worked for an hour, then it quit again. The only factor that changed after the first three months was a change of seasons (the ambient temperature in the kitchen was reaching 90+ degrees F during the day). I don't know if the "blobs" of paste were touching each other when I assembled it, but they were when it failed. How does thick soldering paste start moving around on it's own? With some heat and Capillary action of course :)

Cleaning the board with Isopropyl alcohol fixed the problem, and the clock has been running for the past 6 months without issue.

EDIT 2

When I monitor pin 9 of a 328P on a 5V Arduino Uno, this is the waveform I see.



You can see the small amount of voltage change the oscillator has to make for the 328P to sense it, and function correctly (800mV peak to peak). If the soldering paste is conductive, capacitive or perhaps both, connecting this signal through the paste to ground, power or several other pins can disrupt the signal to the point where the IC fails to operate.