Is There A Dead Cell In My Battery Or An Electrical Problem?

I Recently Just Replaced My Alternator But When I Try To Start My Car, All The Lights Dim And Nothing Happens. Even When I Press The Brake The Lights Dim And All The Gauges Shut Off. Could This Be A Dead Battery Problem Or What? The Car Can Be Jumped But As Soon As I Put It In Gear, The Gauges Will Still Cut Off And The Car Eventually Dies.