3 choices:
1) Your battery (If computer works with AC adaptor, just will not charge battery)
2) The ac adaptor (if Can not power computer w/o battery installed)
3) The input pwr converter in the laptop (converts the 19 VDC to 12 VDC and other low voltages required) - least likely.
How old is the Battery?
(1) Are you able to power on the laptop with the AC power adaptor, or are you just looking at the LED indicating battery is charging. If the Power pack will allow you to power on the laptop, but is not charging the battery, then I would suspect the battery has reached the end of it's life - time for a new battery.
(2) if the laptop will NOT power on using the AC adaptor, then I would suspect the Power pac. Try powering on with and without the battery.
Most of the power packs are universal, that is the output is 19VDC @ approx 4 plus Amps. You can verify this by looking on your pwr pack. The next thing is the connector, believe most use a 5.5 mm plug, but the "Hole" can very. NOTE this is higher than your battery voltage which is prabably between 10.9 and 11.1 Volts.
In lieu of a 2nd power adaptor, you can also use the Car adaptor (if you have one). Just plug into the Cig lighter.