iPod Touch 2nd gen not turning on or charging

I've had my 2nd gen iPod Touch for a good couple of years now, but recently it has just stopped working completely.

I can't turn it on, and when after 2 minutes of charging (on both the USB cable and my DAB radio docking station) it gets extremely hot at the bottom. It is also not appearing anywhere/being recognized if I plug it into my computer, so I can't restore it in any way. It hasn't been dropped in any way, but stopped working after losing battery power and turning off.

I expect it's somewhat of a lost cause due to it being an older gen model, but I would be grateful if there were any solutions available before I take it to my local Apple store next week.

I wouldn't think it was to do with the age though, since I also have a 3rd gen iPod Nano which after a good 6 years or so works perfectly. But, my ask for help still stands, thanks in advance.