How to test if logic board or battery is issue? (MB Air 13" mid '12)

My MacBook Air Mid 2012 recently stopped working unless plugged into the charger. The battery appears to have disappeared, though Apple Hardware Test doesn’t find any faults. Coconut battery doesn’t find anything and the System Information produces:

Battery Information:

Charge Information:

• Charge Remaining (mAh): 0
• Fully Charged: No
• Charging: No
• Full Charge Capacity (mAh): 0

Health Information:

• Cycle Count: 0
• Battery Installed: No
• Amperage (mA): 0
• Voltage (mV): 0

SMC and PRAM resets have done nothing. Does anyone have any experience in whether this is likely to be a battery or a logic board issue? The battery was replaced in May with a third party battery. Is there another test I can do other than buying another battery?

Thanks,

Sam