Ground loops are almost universally characterized by being a low frequency hum, sometimes remarkably pure power line frequency which is either 50 or 60 Hz in most parts of the world.
Hiss would usually be some kind of EMI whether from local gear or nearby broadcast including cell towers.
In general if being battery powered fixes the problem, you just take advantage of the fact that most higher quality battery powered gear has internal batteries and rthey can be recharged via a USB port. You can even find USB cables that provide separate USB plugs for signal and power for negligable money. You then hook a low-buck USB power supply up to keep the battery perpetually charged. Worked for me many times. Take the $100's you saved and invest it in what really makes having a great system worth it - more prerecorded media. Or chase something that really matters like room acoustics or start saving up for a good subwoofer if you don't have one!