That control board looks wet. Before you do anything else, make sure that it is not actually wet. Water will short things out.
To make your thermostat work, take this coiled wire
and straighten it out. Then strip the insulation off the tip and feed it up through the grommet with the rest of the wires. Put it into the screw terminal marked Com24v along with the other wires that are in there. That terminal will then have a white, red, brown, and blue wire in it.
When you put the cover back on the furnace, your wyze should power up.