My kenwood compact disk payer rxd-a53 shut off now it keeps click

Your problem is caused by a blown fuse on the main board 6.3amp 125volt time delay fuse replace with the exact same type. The reason the fuse blew is most likely because they is a problem with the amp.
I suspect one of the finals is blown 2SD2560 or 2SB1647. Open the case and with the power unplugged replace the fuse, next unplug the 4pin connector from the amplifier board 3 black wires and one red.
now plug in the RXD-A53 and turn it on. you should now have the display working and no clicking.
unplug it from the wall and reconnect the 4 pin connector and now plug it back in and turn it on if the fuse blows again take it to a qualified service technician, the above noted output transistors will run you about 6 bucks a piece they are 4 of them 2 of each for each channel plus labor.