My 2011 27 inch iMac intermittently won't turn on

I have a mid 2011 iMac with a 3.4 Ghz processor and 16gb of ram. I had the PSU replaced about two years ago due to a similar issue.

I recently moved house and when I set my mac up upon arrival it would not turn on. I tried the various troubleshooting steps Apple provide with no luck, at this point I assumed I would need a new PSU again and was waiting for a convenient time to get to an apple store.

I figured I would try switching the machine on every morning in the mean time just in case something changed and on the fifth day I was pleasantly surprised that it turned on. Skip forward two weeks of normal evening use and I go on holiday for five days, when I return the mac would again not switch on. Again about 5-7 days later I was surprised to see that it was suddenly working again. Again skip forward about two weeks and once again I am away from my house for 4 days, upon my return the mac will again not turn on!!

The intermittent nature of the problem is confusing me and I was wondering if any has has similar issues or can shed some light on why this may be happening before I lug it to my nearest apple store.

Thanks.