Battery is dead and computer doesn't turn on when plugged in.

Hello,

I have an older Macbook 13", from 2008. This thing has been a workhorse for me for years and I love it. I have replaced the battery a number of times and it's time for a new battery again. However, now it won't power on, even when connected to a wall outlet. Is there something else going on beside the battery or could the battery be so bad that it doesn't even receive enough power to run the device when plugged in to the wall? I am planning on buying a new battery but wanted to know if there is another way to troubleshoot this or turn it on so I can use it before the new battery comes.

Thanks.

I am sorry, I have a 2008 MacBook.