Hi @ericbrandt
Here's the [document|32163|service manual] that may help, assuming the phone didn't get wet or was dropped at all.
Go to p.58 to view the ''Power On troubleshooting flowchart'' and follow that through to see what results.
The manual also contains board layouts to find the location of the components mentioned in the chart and also has a parts list giving the Samsung part numbers and the type of component that it is. If there is a faulty component search online for the ''part number only'' to find suppliers that suit you best.
If it did get wet that is a different matter.