You need to solder both sides of the board , where the bridge rectifier legs goes through, these tracks are joined through the board ,
The blackened area looks like it is not soldered at all ?
I just had the same problem on a Harlem Globetrotters , I couldn't get the solder to take at all, between the board and the legs of the new 35amp bridge ,
the bridge I was replacing (solenoid bridge was blown) ,

I had power coming in to the board , but not at test point, I ended up putting a new 10 amp bridge in, like the original ones were fitted, and that fixed it . As I could solder it properly onto those large tracks .
Buzz with meter between the leg and track to make sure its joined .

Replacing some power supply boards with new ones is a good idea , then you can practice rebuilding the old ones .

Soldering tip: Keep the Tip Clean! important .
if the solder wont heat up , apply some fresh solder and let it melt in .
With those large tracks you need to turn up the iron to about 410 -430 , the other smaller finer tracks turn the iron to about 370 ,
Use a medium size pencil tip . try keep the middle of the tip on the component or track , using the very tip wont get the heat in ,
, and you really need to remove all the old solder , before you re solder new parts back on .
Did I mention keeping the tip clean to that's really important.
Good luck with the machines and the operating