Had one like that. The battery was a dead short. Pulled the battery and it came back. Owner took it home and "tried" again with that battery. They put in the battery and left it on overnight hoping the battery would fix itself. Instead the power supply on the motherboard burned out. Literally. There were fried parts on the mainboard and it did just as yours did.
A new motherboard cured that one.
You can take it apart and put it back together to see if a contact will like the scrubbing action, pull the battery out and try, but in the end a trip to HP/Compaq repair will fix it.
Laptops are unlike desktops. Not much for people to replace.
Bob
Hit power. Comes on, lights light. No video. Shuts down after a few moments. Comes back on after a few moments and does the same thing. Repeats until battery is removed.

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