You will have to eliminate all of the places that can generate static, until you narrow it down to one place. I've had this issue often with electric guitars. It's usually the cord, not the guitar -- but occasionally it has been (like a soldered connection that has gone bad at the jack).
A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort. ~Herm Albright
Yes I tried it with three pairs of headphones (low, med, slightly higher quality) and my computer speakers, so I think the problem has to do with the jack. I found a decently priced headphone amplifier, so I am going to try that out soon. I tested the line out with headphones, and even though the mono output only produces sound in one side of the headphones, the sound quality is much better and much more clear.
No, I got some other stuff from Fiddlershop, but I'm in Canada so getting the violin off Amazon just had faster/free shipping. I contacted Cecilio and am waiting to hear back. If I can get proper audio out of the line out then I'm not sure if it'll be worth dealing with taking the time sending it back to get a new one (and not knowing if another one will have a different, more hindering problem). Thanks for your help though!