Probably not.

Vintage and obsolete products

Apple has discontinued support for certain technologically obsolete and vintage products.

Vintage products are those that were discontinued more than five and less than seven years ago. Apple has discontinued hardware service for vintage products with the following exception:

• Products purchased in the state of California, United States, as required by statute. Owners of these products may obtain service and parts from Apple Service Providers within the state of California, United States.

Obsolete products are those that were discontinued more than seven years ago. Apple has discontinued all hardware service for obsolete products with no exceptions. Service providers cannot order parts for obsolete products.

All retail Apple Stores and the Canadian, European, Latin American and Asia-Pacific operating regions follow the U.S. product list, but make no distinction between vintage and obsolete. When applied to the retail Apple Stores and these operating regions, all products on the U.S. Vintage list are considered obsolete.

https://support.apple.com/en-gb/HT201624

You may be able to try and see if a reset of the Power Management Unit (PMU) can help

since the reset can affect the information set in the chip, and some of that may be related

to the graphics processor...

• Resetting the iMac (Flat Panel) Power Management Unit (PMU) - Apple Support

Another reset that may affect the display and graphics is the PRAM (parameter random

access memory) reset; the instructions on how to perform that, are exactly the same as

those for NVRAM reset. So here's a link that says NVRAM that will reset the PRAM.

The other support article was depreciated and replaced some time ago with this...

• How to Reset NVRAM on your Mac - Apple Support

Also at some point the clock battery on the logic board will no longer support holding

settings of the PRAM and power management unit between power disruptions or

periods of storage. Or at some point when the battery no longer holds 3.6V. It then

would need replaced. http://eshop.macsales.com/item/NewerTech/BAA36VPRAM/

An example of the correct 1/2AA 3.6V Lithium cell is shown ^ here, at fair price.

Be sure to make and keep a suitable external backup of your work files in archive.

There may be some hardware issue, since the model is vintage/obsolete. A service

provider who could deal with these is also becoming rarer; as experienced techs

with hands-on are decreasing in number.

If you need instructions on how to access the battery replacement, or other, ask.

Good luck & happy computing!

FOUND THE SOLUTION:

"replace the RAM!"

tried everything... but when i replaced the RAM. It all worked again! But not the HDMI, since apple replaced my logic board with a faulty HDMI port. Sadly I cant make them repair it again. Those Apple technicians dont know anything. lol Simple diagnostic.

NOTE: Im already on Sierra now! Everything works perfect. Except for HDMI of course.