Look at the battery specs and you find some 300 cycles or about 18 months per battery. So when you bought the machine you are buying into a new battery every few years if you want to run on the battery.
As to cost, your decision on that but there is nothing wrong with a battery that needs replacing every 2 years.
The hard disk is a SATA hard disk which can explain why XP doesn't see it. Can you remember what you did to install XP last time?
You'll find discussions about the SATA BIOS setting all over but telling more about your XP CD vs. your HP restore CDs can remove the mystery.
I have a HP dv5220us with a 12-lithium ion battery for 2yrs now and over the summer the i had i crashed twice ... when i tired to install the windows xp cd its says that no hard drive was found. I got a tech. to look at it and they are telling me to buy a new battery, because my current one has like very lifetime on it, and my ac adapter has a electrical "short".
So my question is should a spend money and get a new battery and an ac adapter or these have nothing to do with my dead hard drive.. or should i get i new computer and just give up on this one.