the voltage output of your new adapter should be exactly same as previous one's.
Such as 19V hp AC Adapter, you'd better only use it of 19V, and the amperage of your new adapter also should be the same or even a little higher, such as 4.74A, you should use 4.74 -4.9A.
If the measure above is useless, and the laptop is still at dead state, then probably motherboard gets something wrong, or DC power Jack has a problem. Actually the latter one stands a good chance, so the motherboard cannot get any power from the AC adapter. In this case, you'd have to disassemble the laptop and replace the DC power Jack. Please take a look at this article: Tips of Laptop DC Jack Repair
Laptop is completely dead, and new laptop battery cannot charge!
When you plug in the oower adapter and press on the power button, but the laptop has no response, no starting sound, no LED light, no fan rotating, except black screen, there's nothing else....in all, the laptop is completely broken, then under this circumstance, what can you do?
1.Ensure your wall outlet is working, which laptop AC adapter could get power from the outlet. But how could you know whether there's power or not? You'd better find a reading lamp with plug to monitor it, check whether the bulb was lit when you press power button. If you cannot assure, then try another wall outlet.
2.Unplug power cord from an AC adapter for laptop, and then plug in the power cord back forcibly, to try turning on the laptop again.Most power cord has a bad connected with power adapter's outlet, which caused the problem, so you should ensure that the two ends of the cord are completely plugged into the wall outlet and AC adapter power outlet.
3.If the power lights still off, then you must change a new power cord and test the AC adapter laptop again, ensure the input voltage is normal, you could use voltage meter to test the power adapter.
4.All right, now our adapter is good, and it could output correct voltage. In this circumstance, unplug the power adapter from the laptop, and remove the battery, then holding press the power button to wait for about 1 minute, after that, plugged into the adapter and attempt starting on the laptop again.
5. Now, your test result is: the laptop still cannot start. Suppose the AC adapter was bad, if you decide to replace it with a generic one, you would have to follow the next rule: