What do you mean by "pc port"?
Assuming that new battery was a good, genuine, compatible replacement battery, and assuming those other chargers output the correct voltage and the connectors were wired the same, it sounds like your notebook's power circuits are faulty.
Running on the charger alone should allow the laptop to run at full performance. The fact it doesn't even do that - with multiple chargers - further indicates the power circuits are at fault. This assumes the notebook is not infected with malware.
If it is still under warranty, you need to contact Dell. Otherwise, I think you need to take it to a reputable shop - it may need a new motherboard.