iMac boots into black-screen, but works after about 10 tries.

Hi!

My Imac mid 2011 - 27 inch won't boot. I hear a chime, the fans and harddrives go but the screen is black.. Though after force-rebooting it around 10 times it eventually gives in and boots. Once it boots everything works perfectly.

As my work station this is of course not something I can't afford to live with if it one day doesn't boot at all. :(

What I have tried:

- Boot with options, single user mode, command+v, disk eject ectect and it does nothing. Just black screen. (until it eventually gives in and boots after about 10 tries)

- SMC and PRAM reset, No difference.

- Updated to El Capitain and did the clean disk 7 times. Did no difference.

- first 3 leds are lit on the logic board when trying to boot. 4th gives no indication.

- Tried to replace the power supply module to a fresh one, did no difference.

- Tried to remove the RAM to see if it could be the motherboard. Had the result of the 2 first leds lit along with a steady array of beeps with an interval of a few seconds.

- Apple hardware test (advanced setting) and disk utility check says everything is normal.

- connected a second screen to see if anything was displayed on it when trying to boot. 4 times out of 5 it would stay disconnected. 1 time out of 5 it gave a loading screen that shifted in brightness levels, loaded halfways and just died into a grey screen.

- Anti virus shows nothing.

When it does boot:

- It sometimes asks me to select a language to install el capitain once it boots (although it's already installed), I just press restart and it reboots into normal.

- Once it's booted, I can put it into sleep, turn it of and even remove the power cable for an hour or two and it will reboot perfectly. It's only when It's been of power for several hours that it starts to give the problem.

Only problem I noticed before the problem started occurring was that my internet browser would sometimes crash. Not sure if it has anything to do with it.

I have no idea what it can be. I have no apple-care and I don't want to spend the money to turn it in to them at this point. Anyone any smarter then me on this? :) Please help!