I have no idea why HP would have told you to run it down to zero - that killed it.
Basically, once an Li-ion battery drops to zero charge, that's it. It is not safe to attempt to re-boot it. The onboard controller will have shut it down.
A professional could try re-boot it using a much higher initial charge, but this is definitely not something to attempt indoors at home. The scare stories of Li-ion batteries going off like firecrackers are not exaggerated. Bypassing the controllers by splitting the cells into their component parts is not even vaguely safe: even if successful, what would you have gained? Half a battery.
Send it to the recycle &and buy a new one.