Except for some rather expected heat damage the bottom looks pretty good, I was going to check the caps and diodes, the electrolytics look ok but there's some ceramic caps on the bottom, tho I would expect them to show some signs of getting hot as too.
a bit of bat of the napkin math says this is a 5v supply with the 820nf capacitor (Also, I cheated, the chip that hasn't had it's markings removed is a syn590r and it's a 3-5v chip). I could try booting everything beyond that resistor on my bench supply with the current limiter turned on and grab my thermal camera

I've got no way of knowing what the rating on that resistor was meant to be tho.
Edit:
ok, my napkin math was wrong, there's a tiny little surface mount 5v regulator on there for the syn590r
I ran the thing at 8v (looks like 12v is what it wants but 8 works) and there's no issues, everything past that resistor works, nothing but the regulator gets warm and the regulator is just being a regulator it's only a few degrees above ambient. With the relay triggered it's pulling 20ma.
So, a 2 watt resistor, I wonder what value... any guesses?
