Okay so, if I were you... and @HiFi Guy knows way more about this than me, but if I were you I'd look at upgrading that cart OR getting yourself a phono stage. Because either of those is going to make a much larger difference than new speaker cables.
The reason for wanting to change my cables is cause the left and right channel keep cutting in and out and sometimes get distorted. Its not the record player cause it happens when the receiver is in the aux or radio channel so its either the cable or (hopefully not) the speakers.
Or its the receiver. If they're both cutting out it's unlikely to be the cables. Cables won't generally cause issues like you're describing, that sounds more like the receiver or the speakers. And since they're BOTH cutting out. My bet is it's the receiver.
I suppose TRY moving the cables so they aren't sitting on all the other cables but it still seems unlikely. I think the speakers are the most likely culprit.
I'm the big dumb. It's the needle. Played around with it and The radio channel works great. The Aux channel didn't work great because the aux cord is broken. I wiggle it and it plays from both speakers fine. The needle is my best guess as the problem now.
Can you VERY CAREFULLY check the small wires connected to the back of the cart? Make sure none of them are loose? I could see distortion coming from a worn needle but channels cutting out completely seems odd.