Does this iPhone Battery look Damaged?

I have just finished replacing my home button and speaker enclosure on my iPhone 4 (GSM), but I'm now beginning to have a charging issue.

The issue is that, the iPhone will not turn on. When ever it is plugged into a charger, it will only display the flat battery indication and the apple logo for roughly 10 seconds, then afterwards, it will turn itself off. (the phone by itself is unable to turn on, hence it is impossible to do dfu mode, powercycle or resets)

Initially, before the repair, the iPhone did not have any sort of charging/battery issue. which is why I'm speculating whether this is the problem or not.

As shown on below images, the battery appears to have slightly been punctured (during repair), but I'm not too sure if this is what contributes to the charging issue.

Otherwise, i may resort to contemplating whether the issue is caused by the prong connections on the motherboard or the dock socket. Here's the picture of the battery connector and dock socket connector (Which doesn't look damaged to me)

So before I try to order a new battery/any other components, I want to seek a bit of input from what people think may be the likely cause of the issue