Laptop screen turns black after a minute when plugged in but is fine running off battery?

Some part of my laptop is dying but can't remember what causes this specific problem- after I turn it on the screen goes black after a minute or two. If I unplug the power cord and just use the battery there are no problems with the screen. Does anyone know what problem this is- I'm pretty sure it's either the power cord connection or the screen/backlight but I can't remember which? Thanks!