Replacing tonearm cable - Dual 604

New cartridge (and new headshell wires), make sure those 8 connections are snug. The hum may disappear, that was it.. If not, that’s good info, keep looking. New cartridge is more incentive to solve it!

btw, the new cartridge can be used on any TT, so go for something you want.

/////////////////////

Brave Browser AI quickie

"Hum on the Dual 604 is typically caused by electrical grounding issues, dirty contacts, or improper cabling rather than motor noise. 

1. Verify Grounding and Connections Ensure the ground wire is securely connected from the turntable chassis to your receiver’s GND terminal; a loose ground wire is the most common cause of loud hum.  Confirm your receiver has a Phono input (MM) and that the Dual 604 is plugged into it, as these turntables do not have a built-in preamp. 

2. Inspect Cabling and Headshell Check that the RCA cables are proper phono cables with correct shielding; mismatched or damaged cables cause significant interference.  Clean the headshell contacts and tonearm pins with Isopropyl Alcohol to remove tarnish, and ensure the headshell is fully seated and locked into the tonearm.

3. Check Internal Wiring If hum persists, inspect the internal wiring for fraying, especially where wires pass through the tonearm. Use a multimeter to verify continuity between the headshell wires and the RCA plugs, ensuring the shield is connected to the outer ring of the plug. Avoid lubricating the motor unless necessary, as the EDS 500 direct drive motor is sealed and lubricant contamination can cause sludge and noise."

9 X/10 this is fixed by replacing the RCA plugs at the end of the output cable. Neutrik/Rean ones from Parts Express are fine if you can solder them on. Old Dual changers had the plugs at both ends, making it easy to just replace the entire cable, but IIRC, the 604 has the internal connection direct to a terminal block. 
using DeOxIt on the cartridge tags is a good suggestion as well. 

Thanks @dynacohum 

I actually did try replacing the rca plugs at the end of the output cable. Same result. It’s not a changer table and so the cable has plugs only at the one end. There’s a junction box of sorts under the deck where the tonearm cable is pinned and the output cable is soldered. 

I’m going to try replacing the cartridge with an inexpensive sumiko while also cleaning the contacts along the way as suggested. Fingers crossed.

The fact that the hum moved to the other side when you reversed the wires, is a clue.

Don't forget the jumper wires inside the headshell, clean, make snug, replace?

I have the 604 as well and experienced the same issue a few years ago when I resurrected it from the basement. Replaced the output cable at the source and the hum disappeared.  It was my first time ever soldering anything.  My bet is that’s what you need to do.  Good luck.