Latitiude E7450 Battery Not Working When Laptop Unplugged

HI All,

Would be amazing if you guys could help me with this.

I have a Latitude E7450 running Ubuntu that will not stay powered on without the mains plugged in. I bought the laptop 26/08/2016 second hand but haven't really been using it until recently (I had a previous issue trying to upgrade it to windows 8 but it was back screening). I cannot remember if it had the issue when I first bought it (logs later in this post look like it may have had). I tried a new battery but it has not helped. 

When I power it on it will turn off within half a second of the Dell splash screen. If I discharge everything it can make it as far as the Ubuntu desktop. One time I discharged it and powered on and it got as far as the Ubuntu login screen but that was a one-off.

The mains apparently charges the battery:

Ubuntu shows "Fully Charged".

BIOS shows as below:

Power events show the following:

ePSA shows the below

Power Stat (Ubuntu App Shows Below)

I have:

1. Drained the battery as per instructions here
2. Reset the BIOS
3. Updated the BIOS to the latest version A22
4. Tried a different AC Adapter
5. Tried a replacement battery from Dell
6. Set Primary battery charge configuration is set to 'Standard' (previously Adaptive)
7. Disabled Multi Core Support (re-enabled after it didn't help)

Don't really fancy replacing the motherboard if that is even an option...

Can someone help or is it a lost cause?