iMac shutdowns when running software

My iMac shuts down whenever I run Adobe Premiere, Elements, or any video editing software, or web streaming software such as WireCast.

While under warranty I got support by Apple. The Tier 3 support acknowledged there was a hardware problem and had me take it to Apple Store to replace the logic board. In Apple Store the techs couldn’t reproduce problem. I told them they had to run the softwares mentioned above. They said they don’t run third party software and refused.

It passed all their test while not under a load. Now it is out of warranty. The Tier 3 who helped me said he told them to replace the logic board or maybe even the power supply. They refused.

Now I have an iMac I can’t use for anything other than to watch TV.

Help! Rufus Echols