Subaru Legacy wagon 07 won't start

[DanH83]

Hi All, bought a used 07 legacy wagon and it was running great. They guy said it had been sitting a while but he started it with a jump and it ran for 20 minutes. I drove it home and a few times over the weekend, it started but seemed a bit weak on startup (understandable). The Battery does look knackered tbf and the terminals are a bit corroded. I went to start this morning but key did nothing when i pressed the button (it was working) and when i put a jump pack on nothing at all happens on turning the ignition on. Is it likely the immobiliser won't turn off due to dead key fob Battery? Would this prevent any life at all or just no starting?