Charger light comes on and then goes out immediately

I have a Surface RT that is a couple of years old now. The battery is almost drained but now when I attach the charger cable, the connector light comes on briefly (less than a second) before going out again and the battery is not charging.

I have tried this with 2 different adaptors which have also both been checked against another Surface RT and they work fine on that one.

I want to try and isolate the issue before I decide what to do next. If it's likely to be a dead battery then I can sort out a replacement but if it's something more integral to the machine then I'd rather not waste my time and money.

Hope someone can help if they've seen this before