New xbox 360 arcade no screen or sound

To start off,what type of cable are you using??
since you've already tried using 2diff TVs,basically its with the console

try using a different AV CABLES, if it still doesnt work,try calling xbox support hotline for possible replacement of your cable or for processing a repair for the xbox if necessary..

since you just bought your console,try going back to the store where you bought it and have it replaced, because for the repalcement of the cable if you call xbox support,it will take 8-12business days for toureceive it and 2-3weeks for the turn around time of the repair for the xbox.