Hi Bob and welcome to Beoworld.
Some of the earlier derivatives of the 3404 had an RIAA inbuilt but I don't know if that applies to the 3404 as it's a US, not European model? Have you tried it without using your preamp?. I've had some turntables that produce hum when not earthed to the amp I've used so you could try an earth lead to see if that helps. What cartridge have you got (MMC 20E/EN?) - you may have a problem with that or one of the connections due to the age of them.
I'm sure some of our tech wizards will have some great feedback for you.
Dave.
Am I ready? I was born ready!