iPhone 4 won't charge Tried plenty of other cables and plugs but it won't charge.

I tried plugging it into a Mac and it's not even detected.

It has had no major water damage; it just simply stopped working.

Replaced battery with new battery, also replaced the dock connector with a new replacement but still no change.

Could this be the logic board? Or is this a lost cause?
Had you previously disassembled or repaired the phone prior to it stopping charging? Why not take it into an Apple Store to get them to fix it?

Assuming you've not made a mistake in your repairs between the battery and the dock connector, yes, it's probably the logic board.