Laptop going into hibernation

"My Dell laptop is telling me it can't identify the AC adapter power source (or something - it flashed up so quickly I hardly saw it!) and then went into hibernation mode. Have we a problem here? Switching off and on again produces the same result!"

This sounds like there is not power left in the battery.   Is it plugged in?  If so, do the lights that usually come on to indicate a/c power or a charging battery light up when you plug it in?

If not, ring Dell.  There will be a service tag on a sticker on the machine, which they will want.  If some bit, e.g. the power adapter, is broken and it's under warranty, they will most likely courier a replacement bit out to you tomorrow.  If it's not under warranty, they will probably sort you out anyway, but just charge you for it.