Power supply problem

I'm having a weird problem with this PC.

To save electricity and reduce the chance of surge damage I normally switch the electricity mains off after I've finished using it. Lately the PC won't switch on if I press the button, unless I let it sit for a while after I've switched the mains on - looking at the back of the ATX PSU, the light that indicates it's getting power flashes for several minutes before settling down to a steady glow, at which point it's possible to switch the PC on. Once it's switched on it's fine.

Any thoughts on what this might be?

If, as I suspect, it's the PSU itself that's on its way out, are the connections for ATX powers supplies completely standardised? The PC is an HP Pavilion, the existing power supply is a Bestec ATX 250 12-Z.

Today I...

...Paid my credit card bill in time to avoid being charged interest.
...Converted my dollar check into a sterling cheque, via a friend who has UK and US bank accounts.
...Discovered that the silver I bought for making electrodes was considerably thicker than the (considerably more expensive) type I've had previously, and about a third the price by weight. The reason being I bought it from a jeweller's supply place, not a chemical supply house.
...Established, with a fair amount of certainty, that the problem with my computer is the power supply (this is good news, it's easy to replace)
...And voted against Boris fracking Johnson

No prizes for guessing which one pleased me the most.

Too much BSG?

I could have sworn that I just heard David Dimbleby use the phrase "Adama and Clinton" on the BBC election night coverage...