I have managed to resolve this issue now - on closer inspection the issue appeared to be the click-wheel on my iPod. There were no issues with the click-wheel component but the connector on the logic board. It looked to be slightly corroded possibly from mild water damage. Cleaning the connector with some IPA has removed the corrosion and the iPod now works! No need for a new logic board. I think the short in the click-wheel connector must have been preventing the iPod from turning on and causing the other components to get hot. Anyway - issue now resolved.
Thank you for all of your help and support so far! I think my new battery will be arriving at some point today so I’ll install it and give it a test. if that doesn’t help I’ve read online that the Power Management IC can sometimes go bad, is this something that can be fixed easily or does it require removing all of the EMI shields? I have a hot air soldering station but I’m guessing a microscope and a lot of care and patience would make this task considerably easier. Thank you, Oliver