iMac 27" Retina (late 2015) not switching on!

I purchased a pretty high spec iMac from the online store about 5 weeks ago and suffered "bluetooth unavailable" faults throughout. These faults came and went until AppleCare considered it a hardware issue. The iMac was replaced pretty quickly.

The second iMac would not switch on at all! I would press the power button and nothing would happen. After numerous calls to AppleCare again, countless SMC & PRAM resets, the issue remained. I was advised to remove all USB connections but this didn't help.

Is anyone else having this issue, esp. with the new iMacs?