Salvage an iMac as an external screen for MacBook

Well... there are kits which allow you to replace the guts and with just the display make a nice external display if that is what you want.

It maybe possible to fix your system, the So called Apple service genius's will often try to convince you a newer system is better. Truthfully for some you just need the old to work as you real don't need the better performance, besides it's only now the M series graphics are better that the AMD GPU's Apple used in this series.

You'll need the tool and adhesive strips to put the display back in either way you go iMac Intel 27" (2012-2019) Adhesive Strips

Just follow this guide iMac Intel 27" Retina 5K Display Logic Board Replacement to Step 18. Then using painters tape place a strip at the bottom creating a hinge and then at the top create two sling straps on the top sides so the screen can swing out about 3" as we will want to place the system upright and look at the onboard diagnostic LED's

Let us know from left to right facing from the front, let's see why the system isn't working.