Is the inverter hooked up through the cig lighter or do you have it hard wired? That's a bad source for noise. I think osny make an adapter for the ps2? Problem may also be your tryin to change power to much 12v-120ac-12.
Try grounding the chassis of the inverter to the vehicle chassis this may help. Or you could try using a ground loop isolater on the RCA cables.
Only sugestions. These may or may not work. You could also try a different converter. You can always return it. Wish i could help more. Maybe someone else will chime in.