It goes down to about 3% before charging will kick in, which defeats the portability aspect of a laptop.
What do you mean it defeats the portability aspect?
Are you saying even when the charger is plugged in, it goes all the way down to 3%? If so, then yeah, there's a problem.
When unplugged, it is supposed to go almost all the way down, then before running out completely, go into hibernate mode so you don't lose any of your work. It sounds like that is what is happening. But when plugged it, they typically are allowed to discharge to around 80%, then charging kicks in to top it off again.
Today I noticed that the power pack is an HP
Yes, HP bought out Compaq several years ago.
Chargers always (1) output a higher voltage than the battery. If you check your car voltage when running, you should see somewhere between 13.5 to 14.4V. This normal even though those are 12V batteries.
And the current/wattage value must be higher than the notebook needs because it must be able to support running the notebook and charging the battery at the same time.
The fact your charger does kick in, suggests it is working fine.
Did you calibrate the notebook to the new battery when you got it? The instructions to do this will be in your notebook user guide. The process calibrates the notebook's battery status monitoring feature with the battery. To calibrate it, you typically charge the battery all the way up, then unplug the charger and run the notebook until it automatically shutdowns and goes into hibernate mode. Then plug in the charger and fully charge it again.
If your notebook is normally plugged in 24/7 for days and days (as mine is) this calibration (deep discharge/charge cycle) should be done about once a month.
If you have never done this, you might want to run through the process twice, then one time once a month after that. They key thing is the battery must be allowed to fully discharge, then fully charge again.
Note this deep discharge/charge cycling used to be necessary because NiCad batteries suffered from "memory effect". And while Li-Ion batteries do too, it is much less prevalent with them. So you just need to do this to ensure the monitoring feature is calibrated to the battery.