Display, logic board or GPU defect?

Hi,

My iMac 24” 2006 won’t boot up. The fans kick in and I can hear the HDD and ODD work as soon as I press the PowerOn button, but it does not chime and neither will the Display turn on.

I already look into the issue and found out that the fault must lie in either the logic board the gpu or the Display (I already checked the diagnostic lights and all except the 4th one light up).

Now my Question is how do I diagnose this issue further without buying parts to swap in? I checked eBay and such and new Parts are mighty expensive. So before I go and spend an arm and a leg on a replacement part, I would like to figure out that it is actually the correct part.

Many thanks to anybody who tries help.

sincerely,

Nicolas