Possibly, easiest way to test would be to try it in another computer with an adequate power supply. But I agree, probably card death. The basic VESA graphics are working to load the BIOS, but loading the driver or initializing the device is causing the system to not boot.
Adapters should be avoided for powering GPUs, particularly one as power hungry as a GTX580.
Upgrading to a more power efficient card would be a good idea in general. GTX1050Ti is about a direct replacement, but a used GTX960/GTX670/R9-280/R9-285 etc is also good.