Here's the [https://www.manualslib.com/manual/1119429/Samsung-Gt-I9100.html?page=36#manual|charging flowchart] from the service manual for the phone.
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If the battery hasn't been recharged for a long while then most probably it has become depleted beyond recovery and needs to be replaced.
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If you want to check if it is getting power to charge, here's the [link|https://www.manualslib.com/manual/1119429/Samsung-Gt-I9100.html?page=36#manual|charging flowchart] from the service manual for the phone.
On p.37 is the schematic for the charging circuit and p.28-p.29 have the board layout.
There's also a parts list on p.9-p.18
Hopefully this will help you to find out what's wrong.
Hi @ellusion
Here's the [https://www.manualslib.com/manual/1119429/Samsung-Gt-I9100.html?page=36#manual|charging flowchart] from the service manual for the phone.
On p.37 is the schematic for the charging circuit and p.28-p.29 have the board layout.
There's also a parts list on p.9-p.18
Hopefully this will help you to find out what's wrong.