There's a good chance its cheaply fixable: Unless subjected to severe overloads TRIACs generally fail shorted rather than open, so if the TRIAC is bad, I'd expect uncontrolled full speed, but you have nothing unless its bypassed. Therefore look for a bad connection and also check if R1 has failed open or C1 has failed shorted, and check the effect of turning R3 the min. speed trim, which could point you towards an open circuit Speed Adj pot (R4). If its anything trickier, replace it.
As you lack experience, to stay safe, do not attempt to make *ANY* measurement or adjustment, or even handle the board, with it plugged in to the mains.