Hi @fixingnostalgia
Here's the [https://elektrotanya.com/samsung_gt-i9100_galaxy_s_ii.pdf/download.html#dl|service manual] for the phone that may help.
When you have downloaded the manual, go to Sect. 8-5 (p.33 of 107) to view the ''Power On'' troubleshooting flowchart.
Like all good manuals it has board layouts showing the location of the components mentioned in the flowcharts and also a parts list as well in case any parts need to be replaced. Search online for ''Samsung (insert part number of required part)'' to find suppliers that suit you best.