I recently bought a new battery for my psp, is my psp dead or is the battery faulty?

As the title states I recently bought a new psp battery, but it's not working. It wont charge, and if I manage to get the psp to boot just from being plugged in, it doesn't even register that there is a battery in. Is this an issue with the battery or the psp itself? Edit: I was able to at least temporarily fix it by adding some electrical tape in between the battery and the cover.