How to ground old turntable with no grounding wire

I would get a wire and touch one end to a metal spot on the preamp and the other end to any metal spots you can find on the turntable like the spindle. Experiment with various spots and see if the hum goes away. If it does then look for a way to permanently attach it. It it doesn't then the problem lies elsewhere.

Does it play? Maybe a wire broke off where it attaches to the cartridge?

Herman, Yes, it plays fine (too fast, actually, but I'm going to adjust that). The cartridge and stylus seem fine. The hum diminishes significantly (but doesn't disappear) when the tone arm is moved off of its rest and onto the record. I like the idea of testing with a wire. I'll try that this weekend.

So probably the cartridge is picking up hum from some other equipment in the vicinity. Try moving the table, rotate it 90 degrees or move it further from the other stuff.

If this is any chance a Grado cartridge, they are notorious for hum. If you post your Table and cart models, it would make it easier to give a good answer. I have several Marantz (6100 6200 etc) all have ground wires. I suspect it would be easy to locate the ground point inside the table and run a wire. When I am messing with them I use a long piece of 20awg with alligator clips on each end. Clip one to the ground on my amp or pre then poke around on various grounding possibilities in the table till I get the best results. Be careful not to short out anything hot though.

I have a similar issue only i made it worse. My wife gifted me a  turntable with shelf(non powered) speakers combo from amazon. The TT has 3.5mm L + R connections in the back. The speakers that came with the TT sound awful. So i decided to plug a pair of yamaha hs50m (powered monitors) to it. As soon as I connect the TT powersupply i get the hum even if the TT is off. However if the plate starts spinning the hum goes away.

So i started googling and visiting boards in which the consensus seemed to be that TT needed ground conection. Sooooo I soldered a wire to the ground labeled spot on the pcb. Grounded the TT to the powerline ground and the hum went away. I felt triumphant until the plate started spinning.... now i get a clicking sound (about 1.5 clicks per second). As part of the trobleshooting i connected the non-powered speakers back to TT, no hum,no clicks.

If i connect 1 powered and one non-powered speaker to TT without turning the yamaha speaker on I get the click through the non-powered speaker until i disconnect the power cable from yamaha.

Anyone has any insights or ideas as to what the issue may be?