Grounding issue with a plastic case

[snk]

Hello
I have bought an old portable multitrack cassette deck. It is in good working condition, but the only trouble is a loud hum/buzz coming from the phono/aux input. The hum is no present if I put the phono/aux volume pot to minimum, but it is very loud as soon as I turn the volume knob clockwise.
I have opened the deck, and noticed that the hum goes away if I touch the input plug with my finger.

So, I think it's a grounding issue, but I don't know how to fix it because : 1- the ground wire from the rca socket to the ground is present, and 2- the device has a plastic chassis (so i can't ground the metal châssis, as it is not in metal).

Is there any solution to get rid of the hum ?
Thank you

[PS : So far, I haven't made the test with a device plugged into the AUX/PHONO input plugs. I have only tested it using jack inputs and phone (jack) plugs]

[PS2 : The RCA plug sockets are all on a separate PCB, as you can see a little bit from the picture attached, but only the PHONE/AUX plug is making such noise... I guess it mayb be because the phono needs further amplification?]

[GibsonGM]

Try plugging something in!  Might be an 'unswitched jack', not grounded with nothing plugged in, which is just open and collecting noise, like some amps have.  That may fix it.    If so, just replace the jack w/a grounding type.

[snk]

Thank you, GibsonGM
The thing is that it isn't jack sockets, but cinch (RCA) sockets, and as far as i know there is no such thing as unswitched rca sockets?
But yes, you're right : I have to try with something plugged in.

[snk]

Wow, I wasn't expecting that : just plugging any RCA plug into the cassette player (with the other side of the cable plugged into my mixer) made the whole hum disappear   

Ok, so case closed : I thought it could be due to some cold solder, ground wire issue, aging capacitor, faulty transistor or something else, but I'm happy to see (or hear) that it's only a "by design" grounding issue 

[GibsonGM]

   Glad to hear it. Ask me how I know that was the likely problem, ha ha.    It's almost always the most basic thing - dead batteries, things like that!