My MacBook only powers up when plugged in; it won't start up in battery mode.

My husband recently backed up my hard drive and reformatted my disk so I could have a clean slate and get my Mac running more efficiently. I was almost out of space. Anyway, now when I unplug my Mac and try to start it in battery mode (battery is fully charged) I cannot start it. I have to plug it back in, start it up and then I can remove it from the plug and it's ok. Any ideas why it won't boot in battery mode? I've never had this issue until my husband reformatted the disk.

I'm running OS X Mountain Lion version 10.8.2.

Thanks!