Connecting powered speakers to a sound card

The line level signals travel this sort of distance through almost any kind of wire, so I doubt the weak signal is anything but a broken wire or bad connection at one end. These are rather high impedance signals, so fatter wire does little good, and increases the capacitive load across the pair and to the surroundings.

However, such signals are only a volt r so, and will pick up less competing hum when running near power lines in the walls, if they run in shielded wire. A shielded twisted pair (signal and ground in the pair) would work best, if the shield is grounded only at the receiving end (shield and ground conductor of the pair connected together at the receiving end, shield unconnected at computer end).

You should be using shielded audio interconnect wire for line level audio. The shield at each end must go to the ground side of the source and destination equipment being connected. The wire should be run where it is not parallel to power wires.