When you connect the charger, does the LED on the Surface charger light up?
Solid white
Blinking
Completely off
Does Windows show:
"Plugged in, not charging"
"No battery detected"
or simply the battery percentage does not increase?
If your Surface Laptop has USB-C charging, try a known-good USB-C Power Delivery (PD) charger of adequate wattage. Microsoft confirms that compatible Surface Laptops can charge through USB-C, although the charger must provide sufficient power.
If USB-C charges it but the Surface charger doesn't, the original charger/Surface Connect connection is the prime suspect.
If neither charger works, the problem is much more likely to be inside the Surface—potentially the battery or charging/power-management circuitry.