Just to add my input since it took me many tries and many hours to ger my clock fixed. I tried all the steps on this post and searched for a long while before I figured it out.
Problem was that my clock would light up for a brief few seconds, then fade out, then shut off. Occasionaly I could press on it, and it would light for a bit. Or, if the weather was near 0, and it was a cold start, it might have stayed on for 5-10 minutes, just taunting me.
Reflowed pins as others have mentioned, I used a pencil style soldering iron, and just reheated the main 4 solder points, and gave some extra as needed. This worked for a bit, then stopped working. After some looking, turns out I needed to reflow the resistors on the back of the circuit board, little black boxes with numbers etched on them. After doing this, and reflowing any solder that looked questionable, problem has been solved for a year now, no issues.
TLDR, reflowing just pins might not be enough, you may need to reflow the resistors, and other solder joints on the board. Good luck!