It sounds like a ground-loop problem. The EMU 0404 has it's own power-supply so it's probably not a power-noise issue. You could try getting an audio isolation transformer, like this one:
The Source By Circuit City : Cables - RCA Audio - GROUND LOOP ISOLATOR ADAPTER
But it will distort the audio somewhat, you can find some that are much better than that one, it's just an example.
You probably didn't hear it with headphones because it's your amp that's creating the ground loop with your laptop. You could also try using a power cord that doesn't connect the third prong on your amp to the wall, but try that at your own risk. It is a violation of a handful of safety regulations that are there to ensure that you won't get electrocuted if the mains inside the amp short out to the case. I suggest just trying that as a test; if at all, and if it eliminates the issue going to your local Audio Shop and asking them for a more permanent ground-loop elimination product (there are many available).
You could also try plugging your amp and laptop into the same power-bar, that may help.