There are no electronics in the signal path.
All electronics are for the operation.
The cartridge could be bad, but I think the hum problem is more likely to be rooted in the conversion to RCA that has been attempted.
There should be a separate chassis ground lead accompanying the two RCA plugs, - it is to be connected to the metal chassis of your amplifier - typically a small fingerscrew near the turntable input sockets.
The leaking capacitor should of course be replaced. I would recommend you grab a servicekit. It has new components for all
electrolytic capacitors (axial, radial and tantal) - new speed adjustment trimmers, a new fuse and a new belt.
PM or email me.
Martin