Try this board on another good machine. Try a known good board and cables on this machine.
Hello. Here is the history;
New-to-me machine (EMC 1989-G5/17/1GB/80/SD/BT/AP/100) with a diagnosis from second owner as trash. Won't boot and display is a mess. After quite a bit of research and trial and error, I get the local Apple store to diagnose 1 bad cap. The tech says that the bad cap is causing all issues and refers me to local Apple repair center. The tech also tells me that this model has already been "fixed" once for same symptoms. I then open the case and find the cap the tech mentioned and see 5 other caps that have been replaced, presumably by Apple in the prior recall.

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