PSU problem?

I'm having a problem that started a few months ago and i'm really worried.

Everyday when i 'turn ON' the PC, right after the first bip, it 'turns OFF' by itself. It's like it does not have sufficient power to turn it on completely.

So i give it a time (normally a few minutes) and 'turn it ON' again. And yeah, it turns ON completely on a second attempt, with no problems at all.

Nowadays, it's kinda rare turning it 'ON' on the first try. And that's whats freeking me out...

I've already done a completely clean up inside the CPU, changed the PSU power cable, and when using it i always keep an eye at the temperatures and voltages; Everything seems normal, And again... with no problems at all.

But, the battle when turning ON my PC persists...;

1- Could it be the PSU?

2- If, i keep "forcing" and keep using the PC like that, will i have a major problem? Maybe on the future? Any Burn component?

Thanks, and sorry about my english.