The pictured bike isn't a "Trek 1274". For that matter, it may not even be a Trek.

The "1274" decals don't denote a model, but rather the number of days Lance Armstrong was out of racing while he fought cancer. When Lance Armstrong rode in the 2009 Tour Down Under, his first race back after beating cancer, it had been 1274 days since his previous race and his bike wore a black & gold Livestrong/1274 scheme in commemoration.

The bike pictured in the ad obviously isn't Lance's bike, nor is it a replica or a special edition that might've been made around the same time. Those would've been newer, carbon fiber, and with higher-end components. The bike in the ad is an older steel-framed bike that someone has dressed up with Trek/Livestrong/1274 decals.

Since the bike's been rebadged and we don't know what it really is, you'd have to take inventory of the bike and its components to come up with an estimate of what it's really worth. We have no idea what the frame is, how decent it is, or what tubing it's made from. But it has a 1" threaded headset and a forged quill stem, which if original, means the bike is likely from the mid-1990s or earlier. The bike has Shimano STI shifters, but I can't tell what model. The pic isn't clear enough to make out much more.