Try this before calling Microsoft Support
Repair Microsoft Surface Pro WILL NOT TURN ON (Battery Not Charging) Studio 2 Book 3 Go 7 6 4 3 Repair Turn
The LED on your Microsoft Surface charging connector glows white when it's connected to a power source. If the LED is flashing white, your power connector or charger might be damaged, or there might be dirt or debris in the charging port on your Surface.
Additionally, your Surface won’t charge if there’s a problem with the power connection or wall outlet. This article highlights seven practical tips for troubleshooting charging issues on Microsoft Surface Pro, Surface Go, and other Surface models.
Microsoft recommends charging your Surface with the power supply that came with your device. You can also use a USB Type-C Power Delivery (PD) charger if your Surface supports USB-C charging.