Constantly going to sleep

My 2007 white macbook is constantly going into sleep mode. It works perfectly for about 3 seconds after unplugging an external monitor, then goes to sleep. The rest of the time it doesn't wake up long enough to turn on screen back light, but I can see it's working with a torch (for about 3 seconds).

The problem happened suddenly & also trackpad button stopped working at the same time. I can use a Bluetooth mouse to operate it.

On startup the grey screen flashes on then the backlight turns off & it goes to sleeps before the login screen.

Anyone have ideas on what needs fixing?

I have reset SMC & PRAM.

Could it be the hardware switch that starts Sleep when the lid is closed, or a software issue?

The battery in it I think has died, would a new battery fix this? I have started it with battery in & out, no difference.

I have removed the hard drive & verified in Disk Utility on another mac.