Same story here, banned night of release. I had a trainer for another Steam game called Control running in background. Nothing related to Destiny No response from Bungie on appeal. I am in the business of customer service, Bungie's attitude of banning without reason and ignoring appeals is absolutely horrible. They need to have the courtesy to communicate, especially with those of us with 1000s of hours invested. People, like myself, who have played since D1 without any cheating, don't suddenly start cheating. I don't even do PVP, lmao.
Using cheats isn’t the only reason to get banned. Simply having the wrong type program open/running (even if not for D2) can lead to a ban. Might help us help you if you list all programs that were running/in use within about an hour of your ban. Plus, you need to give Bungie time to review your appeal. It appears you just recently got banned, so if you’ve submitted multiple appeals already then Bungie will not be too favorable of that.