Desktop PC had difficulty starting...now not starting at all?

Is it making any tones or sounds? I'd try the obvioud first and reseat the RAM, CPU, and Video card.

no tones or noise Brian.

The green light being active on the MOBO simply means that standby power is available.

As Brian stated it's always a good move to reseat everything.

On an anecdotal level, a similar thing was occurring to me and it was because I had some faulty RAM.

What is the exact behavior of your PC when you try to boot it up? Does it begin booting and then fail? Do the fans activate? Or is it simply doing nothing?

Without a tone to go by, the best option would be to reseat all the components and see if that made a difference. Even a small piece of dust on a connector can cause an issue, so remove the components, blow out the pc with air and then reseat the devices. If that does not work, try swapping out with new components if they are available.

along the lines of what everyone else said, you can unplug everything, just try one stick of RAM at a time and the onboard VGA (if there is one), and the keyboard plugged in.  
if you don't get a POST it could be your MOBO, or CPU being dead.  
Check the mortherboard for any spots that would look that something fried.

>>>What is the exact behavior of your PC when you try to boot it up? Does it begin booting and then fail? Do the fans activate?

5 weeks ago,

You pressed the power button. Nothing. Press again. Nothing. Then on the 3rd or 4th attempt. It would start.

Now.

You press the power button. Nothing. Press again...and again...and again. Nothing. No fans only a green LED on mobo.

BTW, Its a Asus P8-Z77 V LX motherboard

Hopefully you have a faulty RAM stick but this kind of behavior "smells" like your motherboard has developed an issue...take a good look at your motherboard for blown capacitors...because there are too many cases of what you should look for just make a google search for "motherboard blown capacitors"... and check if you have a similar case...if you are lucky and it's just a couple of them a good electronic center should be able to replace them for a low amount of money...(after all they cost cents and its a 5 min work)

Sounds suspiciously like a short either bad RAM or mobo short circuit.  Do what has been suggested to test the RAM, if that fails to get results you may have a short on the MOBO.

I found this official troubleshooting guide here that lists a couple of potential options for troubleshooting.

The big thing to note is that your MOBO doesn't have a built-in internal speaker, so you're going to have to install one for this to be applicable.

it can be a lot oif things - even a bad power on switch, or cable
to identify the problem, i eliminate  devices :
disconnect all devices - cd drives, disk drives, external devices
now test if you can get into the bios - or get a screen
if not, remove all ram - leave only one stick and test
herse's how i handle this :
https://www.experts-exchange.com/Hardware/Components/Motherboards/A_1945.html                  (Short-overview-of-how-to-troubleshoot-bad-hardware-when-a-pc-does-not-post)