Laptop keeps turning itself on

I have an old Dell Inspiron laptop. I am not sure why but it now turns itself on whenever the battery is in but the power is off. I should add this is from a complete shut down state, not sleep or hibernate:

Laptop power lead plugged in and on and battery in - laptop stays off when switched off
Laptop power lead plugged in and off, and battery in - after 2 or 3 seconds the laptop switches on
Laptop power lead not plugged in and battery in - after 2 or 3 seconds the laptop switches on
Laptop power lead not plugged in and battery out - laptop stays off when switched off

If it switches itself on, it goes to a black screen giving me options on conducting a repair, a restore, entering safe mode or starting normally - I have tried repairs and system restores with no joy.

I have tried looking at the BIOS to see if there is a way I can turn off any wake-up functions. However when I view it (F2 on start up), the only options I am given are Main, Advanced, Security and Boot, non of which let me change anything relevant (Bios is A11, Aptio Setup Utility via Dell inc).

Any advice appreciated.
Regards,
Ben