Hi. This is an odd one. My 2004 1.2 dualogic Panda's stereo is turning itself on and off constantly until it flattens the battery.
All I've done is replace the battery.
Thanks in advance.

There have been similar issues previously about these. They (the radio) seem to die, sometimes randomly turning on, or often just draining the battery.
Usual fix is to bin it and fit an aftermarket unit. To do this properly you need a CanBus adaptor.
Do some searches and have a read through what others have done.

https://www.fiatforum.com/punto-ii/356857-radio-turning-when-car-locked.html?p=3542517



If you can live without a CD Player remove the micro switch.

Probably need unsoldering. But not sure. Local repair company will probably do it for you. If you don't have the equipment and or skill.