Bridge Rectifiers fail due to age and use. They have a pretty tough job to do (converting AC to pulsing DC), and being that yours is around 20 years old, it's not surprising that it has failed.
The Cap should be replaced too, as it smooths the pulsing DC into proper DC that can then be used by the electronics further down the path. Electrolytic Caps eventually dry out (the electrolyte drys out), and therefore cannot do the job of smoothing the pulsing DC properly, which leads to random and strange problems later on.
The voltage coming out of the transformer is most likely OK as transformers rarely fail, but a good idea to check it just in case.
