Low-Level TT Hum -- Suggestions?

I have a Systemdek IIX turntable with a Signet MC cartridge mounted. I bought it very broken -- it had been poorly packed from Ebay to the new owner. The glass platter had shattered, the original cartridge was broken (by the platter), the motor shaft was snapped and the dustcover was destroyed. It still has the original Profile-branded Jelco SA-250ST tonearm installed.

I've brought it back to life and it's been a delight, but it has always had a low level hum. My old speakers apparently diminished the hum. I was always aware of it, but it wasn't too blatant. I got some electrostatics and it's now unbearable.

I know a lot about the mechanical portion of the TT now, but I'm lost as to what to do to diagnose this ground problem. The only other humming deck I've had was the classic "Grado cart on a Rega" issue.

So far I've looked at the overall ground to the preamp, which seems fine. I notice that when I touch the metal RCA plug housings on the TT interconnect, the hum gets louder. That's as far as I've gone.

Can someone suggest some stuff to look at and/or test? I'm comfortable with a multitester but I don't know where to start.
Grounding out hum

different preamps have different grounding arrangements. If this turntable hums a little, and others do not, then the turntable is at fault, follow instructions above. My turntable has a separate wire to ground the headshell and arm to the preamps ground, which is the metal case on both the PAS2 and the RA88a preamps. Both preamp devices have 2 wire power plugs. I get a little less hum when I also ground from the same screw of the preamp case, to the third pin of the power strip, using a surplus nema connector with no power connected to the flat blades. More modern designs might also have the case grounded in the 3 pin power plug-check with a meter.
Problem Solved!

Pretty much all the stuff you guys suggested was already done -- the grounding was all good, even to the motor shell, all the connections in the headshell were snug, etc. I used a needle to snug up the connections in the female end of the DIN plug where it connects to the tonearm, but mostly I built an RCA box to attach to the back of the table. I mounted two RCA jacks in a little metal project box and ran all the grounding to the box with one ground wire coming out. I cut off the stock signal cable at about 6" and hooked it up to the RCAs. Cost me about $18 and lets me use better interconnects AND avoid paying $60 plus shipping for a high quality replacement DIN cable. No more hum.