I saw this old thread while googling a solution for a similar issue - my mac mini would not boot at all, after the apple logo the screen will go dark and come back up as a frozen white screen with subtle vertical lines.
So if anyone comes here still looking for a solution, I managed to fix mine today after taking it apart. The thermal paste on the GPU chip / heatsink was very brittle - cleaning and replacing that alone most likely would've fixed my issue, however I went one step ahead and used a heatgun on the chip for a couple of minutes to reflow it. Baking the entire board seemed a bit overkill since it's clearly the GPU chip alone causing the problem.