charging a HP is 14"sleekbook battery externally

After 2 years? You may get really lucky and be able to get it to charge. But that is a big maybe. More likely you would need to replace the battery.
 
Unless HP specifically made an external charger for that battery, I would not recommend DIY-charging it - your house and your life are there.

What do you call "power cord" - the whole stuff from power outlet to the laptop, or just the piece from the outlet to the adapter? You can find compatible power adapters for next to nothing