If you bought it from a reseller, and it is the same as cited OEM at the Apple Store online, that would be the correct battery... though in some locations there may be a different product number or an old-spec battery.
Here's the Apple Store US page for OEM replacement:
http://store.apple.com/us/product/MA561LL/A/rechargeable-battery-13-inch-macbook -white
There would be a different part number for a black replacement battery, where available. I've seen amazon resellers and ebay sellers offer part numbers; some are clones. Others are third-party replacement.
white http://eshop.macsales.com/shop/apple_laptop/batteries/MacBook_13_White
black http://eshop.macsales.com/shop/apple_laptop/batteries/MacBook_13_Black
Note the 'Model Identifier number' for your MacBook as a partial way to determine parts and software.
The battery you received may have been defective. Did the computer run off the AC Power Supply? If it can, then you could try & reset the System Management Controller, to see if that teaches it a lesson.
•Intel-based Macs: Resetting the System Management Controller (SMC)
http://support.apple.com/kb/ht3964

Sometimes if you can't get a rise out of a Mac, a NVRAM or PRAM reset may help.
About NVRAM and PRAM:
http://support.apple.com/kb/HT1379
Hopefully your MagSafe adapter is OK, and the MagSafe Board, too.
Check to see if the magnetic connectors are clean & dry.
Good luck & happy computing! 🙂