Windows 7: Power button not working properly

When I press the power button to power the PC on, it's not working. If I use the on/off switch on my PSU and then press the power button quickly, the PC starts up. I usually do this for a few minutes before I manage to power it up. I've had the PC for a few months and the issues started last week.

I opened up my case and made sure everything is connected properly.
If the PC is on and I press the power button, it turns off just fine, so this means is connected properly.

I think it might be an issue with my PSU, but I'm not sure.
Any tips?

It might be a lot of things. Your power switch, your PSU, your motherboard...

Start small and work upwards. The first thing to try is to isolate whether the power switch is causing a problem when you first press it. Unplug the power switch from the motherboard's pin header, then, using a small screwdriver, carefully short the two pins that the power switch plug was attached to. You don't want to do it for very long. If the power switch is faulty, the PC should kick over and start right away. Voila, problem solved. If not, then you may have other issues.

But please try that first and post back with the results.

Oh, and while you're inside the computer, this would be a good time to check all of the power connectors and make sure that they are firmly in place and secure.

As Mellon Head says mate but it could also be a fault in the PSU ? maybe the Power_Good signal so give this a whirl
Using HW Info
PART A:
You can test the volts on the PSU with HW Info HWiNFO, HWiNFO32/64 - Download < download the right bit version and close the right hand window select Sensors and scroll down to the power section where you will see what the volts are doing see my pic. In my pic the section (Nuvoton) with VBATT as a dead give away you are in the section for the rail voltages. There are other section titles and one that pops up often is ITE (sometimes the usual one for Gigabyte boards)
Now the voltage on the different rails have to be within 5% =+/- of what is required or the machine will not work properly if at all.
Limits +/-
12v = 11.4 – 12.6v
5v = 4.74 – 5.25v
3.3v = 3.135 – 3.465v
The Power good signal voltage at pin 8 on the 24 pin plug (grey cable) should be the same as the 5v rail reading/s
See this for the rail voltage info
PSUs 101: A Detailed Look Into Power Supplies (Section 2.)
The original right hand window shows the machine running and is handy for that but for looking at the components in some detail close it and use the main left hand side panel
FOR OTHER COMPONENTS
PART B:
Open each small square with + in it on the section the components are in and then click on the individual component/s (it will highlight in blue) - in the right hand side will appear all sorts of details including brands speeds and other essential info that particular device. See pic for example.

Edit: Menat to add test the volts at pin 8 (grey cable) on the 24 pin plug - should be around 5v

Had this exact same problem a few years back. After a lot of screwing around, found the video card was the culprit. Tripped out the PSU 9 times out of 10 on start.
Art

So how did you fix the issue? Replaced the video card?

Stranger things happen at sea they tell me but pretty strange things go on in computers too eh?

As Mellon Head said, it could be many things. The PS has a +5V (pin 9 of the power connector) that is always on (5VSB). When you press the start button an output signal from MB is sent to the PS to start the other supplies (12V, 5V etc). As the same start button is working to shut it down, I would discard the button. As you also said that if you switch the PS off and then on and quickly press the start button, it stars, it can be the PS or the MB. I will guess that the 5VSB starts for a short period and then goes off, and you're not able to start the PS other supplies and the computer doesn't start. If you have a Volt meter, measure the pin 9 related to ground (pin 5) to see if you have +5V before you press the start button.