I have an older but similar Logitech system, they use way less than 500W. Depending on the computer PSU used, it could cause issues if the load is too low. But for a quick short-term fix, I'm sure it beats no sound.
What problems did the Logitech PSU have ?
To Deeptarup, it could be something like the muting circuit. I know on my old logitech, the main output chips, have a little circuit that can mute the output, on startup, and when headphones were attached. And for thermal shutdown too, it did a thing like that.
Does is do anything at all ? Or just no sound? If you crank the volume, is there hissing or anything ?
It could be a lot of things, from the PSU, to the op-amp's, to the output. Do you have a multimeter ?