I'm not going to answer the question you've posed - Tony Stewart has done a good job of that.
I'm going to address your assumption that those capacitors have leaked.
Capacitors and other parts are often glued into place in audio circuits. If they could move, then they could cause noise. Sometimes, in an effect called "microphony" parts will pick up sounds or vibrations and inject them into your audio. If the parts are glued in place, then they are far less likely to cause problems.
Large parts (like your capacitors) can also break off from their own weight if the board is accelerated violently (say, dropped on the floor.)
Your capacitors appear to be glued down. The glue is often a brownish color as in your pictures. Also note that it only extends a couple of millimeters around the part. If it were leakage, it wouldn't be as evenly distributed.
The electrolyte is corrosive. If the stuff you see were electrolyte, the wires on the parts that have brown stuff on them would be greenish (copper turns green when it corrodes.)
Finally, those capacitors appear to be in the powersupply. If they were the cause of the noise, it would cause noise on both channels at the same time.
So, I think your problems lies elsewhere.
I would check the volume control and the connectors for the noisy channel. Wiggle the volume control and see if it causes noise. Wiggle all the connectors and see if they make noise.
After that, flip the board over and look for solder joints that have gone bad.
Often times on old equipment, you will find a part with a leg that has a "ring" around the pin where it comes out of the solder on the back of the board. Heat and vibration weaken the solder, and the pin breaks loose. It isn't soldered any more, but it still conducts, because the pin is still mechanically in contact with the solder. Vibration causes it to lose contact, and you get noise.