I have to say I agree with Tinsy, although I do not claim to be any sort of expert.
Simply, the tube that has snapped has not been welded onto anything. It’s part of a complete tube which has the top-tube and seatstays welded onto it.
As you’re not the original owner, you’ll not get a warranty claim. Also, from my experience as a former Trek dealer, they won’t deal with you direct.
You’d be best taking it to your local Trek dealer and seeing if they can sort you out with a reduced price replacement through Trek. You’re in no way entitled to it, so I wouldn’t be that surprised if they say no. However, it’s of benefit to them if you keep riding their bikes, so they may be willing to work something out for you. Having dealt with them a lot in the past, they’re a pretty reasonable company and they’re generally pretty accommodating.