Yes, be careful. Heatsinks in SMPS can be live, not only by accident, but by design. And keep in mind that the main filter cap can store hundreds of volts for some time after you disconnected the supply, discharge it before you touch anything on the pcb.
In an ATX power supply and the majority of other SMPS's you will find MOSFET's as switching transistors not bipolar transistors and MOSFET's usually have source and body terminals connected together internally (sometimes drain and body):
Although the MOSFET is a four-terminal device with source (S), gate (G), drain (D), and body (B) terminals,[1] the body (or substrate) of the MOSFET is often connected to the source terminal, making it a three-terminal device like other field-effect transistors. Because these two terminals are normally connected to each other (short-circuited) internally, only three terminals appear in electrical diagrams.
Now why would you ever need that third pin then? Well, often you can't have a live heatsink, maybe for safety reasons, maybe you have other devices mounted on the same heatsink that have a different potential on their tab. In that case you have to isolate the tab from the heatsink, by using a sil pad for example, or you can buy transistors with isolated tab, but now you obviously need a third pin to connect to the source.
And for why your power supply isn't working any more, I'm no expert, but your power supply may have several MOSFET's paralleled up to increase the current handling capability and one of those transistors might have died when you pushed it, because cheap ass ATX supply probably don't implement paralleling very well. Or your electrolytic cap's have gone bad. At least those two things come to my mind.