It would appear that there is a discrepancy between the schematic callout and what was found on the board, so far as the capacitor’s concerned; the 394J marking would indicate a 0.39uF/5% device, whereas the 0.27J callout would suggest a 0.27uF/5% part.
The transformer’s a tougher nut to crack; at board level it is very common for these to be made to order as custom items, rather than selected from a list of standard products. As such, the markings/marking systems are often proprietary, rather than anything useful for identifying potential replacements. Reverse-engineering such things is a possibility, but for a one-off application the time & effort involved would likely make it more feasible to simply replace the unit as a whole.
Beyond that, the level of burnination shown in the photo makes it very likely that there are issues beyond the obvious that would need to be rectified in order to make a successful repair.