Inspiron 1440 Battery Charger Port Failure

I have an Inspiron 1440 which I purchased in 2010. Recently I noticed that the battery charger port (round, on the left side) no longer recognizes when the charger is plugged in. I can plug it in but the battery doesn't charge. For a while, if I pushed the charger into the port very tightly the battery would charge. That no longer works.

The battery itself is not the problem. I replaced it 2 years ago (2015), and, as I said, it used to charge when I gerry-rig the charger. 

I called Best Buy, where I purchased the laptop originally; they said that this particular model has a charger port that is welded to the motherboard, meaning, it cannot be removed or replaced. They advised me to purchase a new laptop. Is this the case, or can the port or charger plug possibly be repaired or replaced, without my needing to buy a new unit? The laptop works perfectly other than this problem; I realize it's 7 years old, but I don't want to buy a new one if I don't have to.

Thanks.