Sadly, your dedicated GPU has failed!
Running Target Disk Mode only leverages the CPU intergraded graphics (IG) engine. while your system trying to boot up starts off running the IG, during the boot at 2/3 mark the system flips over to the dedicated AMD graphics card (DG).
Here’s the steps to replace it: [guide|6272]
Getting a new part is getting hard and used boards are iffy! You could try baking (or heat gun) your board to see if you just have a cold solder joint.
But before you go down this path make sure you have an external backup of your data.