Replaced my PSU & there have done 10 reboots or so, but as of now no self reboots.
Keeping my fingers crossed for this to be the final solution to the problem.
Now, in case I wana give away this desktop & do not want to format the HDD; what all should I take care & remove, apart from copying & then securely deleting my files with CCleaner Secure Deletion DOD 5220.22-M (3 passes).