My approach would be: disconnect the battery and connect multimeter leads to the battery connector on the motherboard. Then, plug-in a charging cord and look for voltage (might not be continuous, could be pulses). If the motherboard is putting voltage to the battery connector, then you can assume that the issue is with the battery itself. If the motherboard is not putting voltage to the battery connector, then you may have a damaged PMIC, or a short circuit on the charging system.

It's my understanding that this is a pretty widespread issue with the Note 10 and the Note 10 plus. I've attempted to address this issue with several customers and here's what I've learned… The connector that attaches the NFC coil to the motherboard breaks connection with the motherboard. This is something that will need to be handled by a shop that performs microsoldering. It is still possible that this issue is caused by a faulty thermistor on the wireless charging coil, but in my experience (five devices all with the same outcome), it has always been a motherboard issue. I would like to see Samsung step forward and address this issue, as it seems to affect a large enough percentage of these devices.

Learned this while replacing the digitizer connector on an iPad mini board: It's a LOT easier to remove and replace SMDs that are in the way during board work, rather than trying to maneuver around them with your iron. Also, to avoid having to replace (lego type) connectors on boards: first, press down gently on the FPC connector and rock it a little to create a little movement. Then, lift from the smaller side of the FPC connector. I was replacing quite a few board connectors before I learned this.