Power Supply Hiccupped

This morning my Power Supply started and stopped several times before catching and running fine. Needless to say that I leaving the computer on for now.
Does this sound like it is beginning to bite the dust?

 

Absolutely.

While I understand your reasoning here -you think it may never turn on again- I personally think you should do the exact opposite! Turn off the PC and leave it off until a suitable replacement power supply is acquired and installed. Running your PC using an obviously failing power supply is not a good idea, and it may cause damage to your components. These damaged components may get "conditioned" to run with the failing unit, so when a healthy new unit is installed, your components get fried by the healthy juice because they've been "conditioned" to run with "unhealthy" juice. I've seen it happen. A dude I know knew his PSU was failing, but he kept pushing it and pushing it, even after the fan in the PSU quit spinning, he kept going. His reasoning: "as long as the computer still runs, there's no reason to buy a new power supply while this one still 'works'". Well, this PSU eventually completely died. He installed a new power supply, and the PC ran for 2 days before the motherboard and video card failed. Had he replaced the PSU right away instead of milking it for 2 months, he could saved over $200.

 

the fan started and stopped or the whole system ?

 

Quite often intermittent faults in PSU's can be down to dry solder joints, I've repaired quite a few over the years with much success.
The problem seems to be getting worse these days as we have to put up with this lead free solder garbage.
I normally pump all the lead free stuff off and replace with real leaded solder.

 

Have you recently added or upgraded any other hardware?

I agree: fork out the relatively few bucks to get you a new PSU - it's right up there with RAM as the easiest and best computer overhauls...

 

I purchased a new PSU, but for information-It starts up and shuts down within a few seconds.

 

Try starting it up with just the mother board connected on it's own and see if it starts up then if not you probably have a bad mother board. It's possible you have a capacitor gone high ESR.