Powering ESP8266 from pc atx power supply
PC power supplies are unstable when they only have a low load. You can convert a PC power supply into a stable source of low current power but you need to add a dummy load.

Instructions on how to do this are here: http://makezine.com/projects/computer-power-supply-to-bench-power-supply-adapter/

Given the risks involved in modifying a PC power supple I would recommend finding another source of power.