Selected ESP8266 WiFi modules short out ATX power supply
It certainly sounds like you have two fried ESP8266's. 
To add some more to Chris's and Peters comments above:


If you don't have minimum loads on the ATX power supply your rails may be out of spec, and typically they will be high. By how much they are out of spec is an unknown, but it could easily be 10% or more. On the 3.3 V supply this would take you just outside the ESP8266 absolute maximum of 3.6 V.
Most ATX power supplies have what is called cross regulation, so the +3.3, 5 and 12 V rails don't have independent regulation, it's ratiometric. 


Here's a graph of the rail association for a typical 220 W ATX power supply:

 

Notice that there are minimum currents specified for the +3.3, 5 and 12 V supply. If you don't have these minimums in place then the supplies output voltage becomes questionable. If you have a more expensive supply it might gracefully shutdown, but most cheaper units do not. 


I don't see any problem using an ATX power supply for hobby/bench use, after all the other choices might be to have an adjustable 30 V, 5 A bench power supply which is just as ridiculously over powered for an ESP8266 as an ATX supply.
If you are going to use an ATX supply it might be prudent to fit output current limiters so you can adjust current limits down to suit the devices you are powering.