There are actually two batteries or in some cases one battery, and one capacitor. One supplies obviously the power when you turn it on, and it is not connected to a plug in the wall. The other supplies certain system settings and affects the PRAM. The latter if not replaced after 4 years can give conniptions to everything else. So depending on how old your Mac is, you may be faced with its demise being replaced by the main battery as a source for those settings. That second battery or capacitor is called the PRAM battery, CMOS battery, or Clock battery. Check where you had your battery replaced if they looked at that one or not.