The dishwasher will not turn on

Congratulations - you found the fault !

The options you have are -
Buy areplacement board from a spares centre.
Buy a take- off board from a scrap one on Ebay.
Or - Learn about electronic repair - and identify the burnt component , buy the parts and replace it yourself.

You can take it to an electronic repair shop - if you can find one - or a electronic supply shop - and ask for a new one of "them".

If replacing a burnt component - often there is a cause other than just that component.
Experience tells you what else might be wrong to cause it.