Let The Fun Begain, New build on the Table.

[JAZZCNC]

Ok well first before you start ripping it apart just do some better cable management.

Separate the signal wires from the Power wires and run power cables together.
Don't cable tie the signal wires together just run along side each other lose.

Shielded cable is the proper way and should really be used and like Swarf says just buy CY cable if you do.
You'll find it here cheap enough and just use 4 core 0.5mm or 0.75mm. CY Cable
Only ground one end at the control box and make sure your control box uses star grounding. IE all grounds to same spot.

But it doesn't always follow that because you haven't used shielded cable you'll have problems it could work fine but you are much more open to interference and corruption of data signals without it. . . . I suggest you try machine and if any strange happenings like Z axis lifting/dropping or false limit or E-stop signals then you'll be getting noise on the lines.

Regards which wires to sheild then it's motors and limit cables, any cables that send signals. Following on from above, if you have trouble with noise then chances are it will be the limit cables that cause it because they tend to be the longest run, effectively acting has a big antenna sending and receiving signals. Similar applies to the Stepper cables because they are long.

Main thing is to keep power cables away from signal cables and shield any signal cables. This esp applies to spindle cables if your using a VFD which are very noisy things.