Leaking components on a circuit board would typically be electrolytic capacitors. For cansiter types, there are typically 3 indented pressure release marks, see if these are bluging outwards or cracked. Otherwise they may have leaked around the wire end mount and the leaks should be visible around their PC board mount point.
This is quite common on lower quaility components but is not uncommon with age. To find the power input, locate the largest electrolytic cap (the bigger black things with -ve symbols) and follow their copper trace from underneath - or you can try using a multimeter with power unplugged and use the resistance or continuity setting but following the trace is better.
It is possible a cap may have gone short and blown a fuse too.