A little more information would help a lot actually..
Did you recently install the wpa_supplicant package?
Did you update your system recently?
Is this a fresh install?
Have you auto enabled a wifi profile lately? May something be wrong with that profile?
How long have you waited since the output on the screen says "Started WPA Supplicant" and did it actually go "success" and says "started" or "starting".. Is it still like that or did you turn it off?
Based on your other recent question here i assume you are running Arch Linux, would you be able to boot with the installation medium of Arch and chroot and disable/remove wpa_supplicant, and then try to boot your system again? Might be a broken package.. Have you checked bug tracker @ arch website?
Also, you could try to diagnose the hardware, (RAM and HDD) with Memtest and gsmartcontrol(smartmontools) (long shot, but still possible..)
I won't apologize for asking more questions than i replied with answers since your question is extremely vague.