I'm sure you've done all of this but let me wing it anyway. Brainstorm fashion, in no particular order other than the minimum config step.
Remove all input sources from your preamp. Is the am radio RFI gone? Is the 60hz hum gone? If so add one input source at a time and see if either symptom comes back.
It it does hopefully you can ID which source caused it. If neither returns maybe replugging everything cleaned up an oxidized input jack. If its just your TT is it grounded? Is the preamp properly grounded? Do you have a common ground in your system? Is the preamp picking up stray magnetic fields from being too close to another
component. Try shielded cables as you mentioned too. My best sounding cables were
also an unshielded pair. Sold them and made some DIY cables out of BELDEN coax...work great and not a hint of AM radio or hum. More thoughts...are the cartridge leads in good order, no breaks inside the tone arm, etc? RFI can be tricky. 60hz hum can be equally frustrating. Good luck and let us know what happens.
One more thought...google shorting plugs...for the unused inputs.