I have got an old laptop (HP Pavilion DV2000, 5.5 years old) and I just bought a new battery for it (10,8V 5200mAh 6 Cells) probably not an original one.
When I charged it full the first time, it reached a capacity (as see through the Ubuntu 12.04 Power Statistics tool) of 80%. After 3 full cycles, it's at 79.5%.
Do you think it is normal, or the battery may be damaged (and I can complain with the vendor)?
Chances are it's a bad battery. This can occur, especially with aftermarket/non-OEM parts. (I had one that wouldn't go above 92%.) There may be official battery life or battery load testers, but a simple way to check would be to turn off power management (so it won't suspend the computer on low battery) then run the battery completely dead and recharge it. If it still won't take a 100% charge, I would complain to the manufacturer.
HP mentions calibrating the battery.
There is an option for battery calibration (before windows boot): ESC then F2 will get you to the right menu
There's a chance that this is a setting in the laptop's charger system. Many laptops (such as my Sony) have a setting that limits charging of the battery to 60-80% to prolong battery life.
The setting wouldn't be in the standard "power options" menu that equates to the Windows one, but would be in a HP-unique menu (that you might have to boot up Windows to access).
Sounds like the battery/or charger isn't switching over to a trickle cycle (or it's not really a new battery pack.)
Most lithium-ion polymer batteries use a fast charge to charge your device to 80% battery capacity, then switch to trickle charging. That’s about two hours of charge time to power an iPod to 80% capacity, then another two hours to fully charge it, if you are not using the iPod while charging. You can charge all lithium-ion batteries a large but finite number of times, as defined by charge cycle.
from: http://www.apple.com/batteries/
Note: The quote and URL point to an Apple site, but the information applies to just about any Li-Ion battery.
