I concur with the performance statements above. Typically if a battery has died from old age, the MacBook has been able to power-on (though slow).
I have had one exception: one MacBook refused to power-on, which contained an off-brand battery that had failed. That one MacBook had an extensive history of physical damage and repairs, so I do not know if something in the computer's history was the culprit or the use of an off-brand battery. Regardless, it regained full functionality when I replaced the battery.