I bought a Deskjet 3520 but it would not turn on reliably so I took it back and they gave me another one. The second one will not turn on reliably.
Please don't suggest all the normal stuff, I know what I'm doing and I have done all that.
The only way to get it to turn on almost reliably is to pull the power cord out and re-insert it while holding the power button down. It turns on about 4 times out of 5 when I do that. The auto power down is set to "Never". If it goes into the sleep mode with the power light glimmering on and off it will turn back on at least in the short term. I have not ried to leave it that way for a long time yet.