There are too many reasons to pin point particularly without seeing how you have it connected. I blew a couple of 317's by mixing up pins or mishandling the output. Another one I blew because the breadboard wire fell off my hands onto the board. So check and double check before flipping the switch is a good thing.
ATX is not a good choice for newbies like us. I am not an experienced ee-guy hence I said us. I am just a few car lengths ahead of you but by no means an expert. The reason why NOT the ATX: First, some ATX design is unless you have a certain size load, it doesn't turn on. Second, ATX pumps out too much current - enough to melt a breadboard (and I have one with an 8pin spot melted by the overheated OpAmp powered by 4AA (Eneloops). The battery clip also melted).
Experiment with a power supply that has current limit as well as volt limit. You are better off using a 9V battery. 9V battery pumps out only 200-300mA max so it limits the danger. Another alternative is the CC/CV boards. CC/CV typically are current-limit rather than constant current. I use that as a low cost substitute. Not great, not even good (high noise, not reliable...), but better than an ATX.
Oh, get the rechargeable kinds, then you can re-use and re-use.