You'll probably want to re-solder joints of big components like relays, or whatever looks visually bad. It's a dryer, I assume it spins at fast rpm, so you may also have vibrations, so you may have cracked solder joints or weak solder joints.
Check output capacitors, check diodes, replace the IC ... not much else you can do.
Alternatively, you could just figure out the output voltage (probably 12v because of the mechanical relays) and replace the whole thing with a classic transformer and a linear regulator, or a pre-made 12v power supply. It's not like you really care about the efficiency when you're washing so what's a couple watts wasted while washing, so even a classic transformer would work ... pcb transformers are relatively cheap, under 5-10 eur.