Dead battery won't jump start

Helping a friend with her car. It sat all winter and is dead. Tried to jump start, dome lights come on but all it does is click a few times and goes dead. Leave jumper cables on for a few minutes, dome lights come on, few clicks and goes dead with all lights going out.

Can a battery go so dead, that it cannot be jump started? I seem to remember that happening before. Someone told me starter, but I am thinking with it sitting all winter I am going with battery first.

Any thoughts?

Thanks. Put a new battery in and it fired right up. The dude that told me it was the starter should be ashamed of himself (a neighbor)....LOL