HP laptop problems (PART 1)

One of the laptops I have at home is an HP dv6000 laptop. The laptop looks great. I like it's design, characteristics and price. I was very happy with it (and specially my girlfriend as my main laptop is my MacBook) until the problems started.

First problem: beeping

Even though it was definitely shut down it would just start spinning the fans at maximum speed and beeping loud. The only way to stop it was by removing the battery. This was very annoying and specially when it happened at night. A friend that had a friend that had a friend that worked at HP support told me that it was a known problem and could be solved by updating the firmware. I updated the firmware and it went way.

Second problem: cannot read CDs

A few days later, another problem. While reading a DVD (or was it a CD?) the computer hanged. I forced a restart just to find out I could not read any CD. DVDs worked just fine. I phoned HP and after reverting the laptop to it's default configuration with no results (as I expected) they took the laptop for repair and returned it a few days later. Support was really nice as they went to my office to pick it up and then returned it again there.

Third problem: no wireless card

I was happy with HP for having fixed the laptop so quickly and efficiently but that didn't last long. Suddenly the wireless card just stopped working. It started working intermittently but it eventually gave up working. It not only stopped working, the operating system couldn't even detect any wireless card present (it is an integrated wireless card). HP support was once again quick and efficient with the repair the returned it fixed.

Forth problem: does not turn on

This is the most recent problem and it happened twice. I'm not sure yet how it happens and how to fix it but I have a clue. My guess is when I leave it sleeping and unconnected to power for a long time, the battery is consumed. When it is completely discharged, the laptop does not turn on even if you connect it to power. I managed to revive it both times but removing the battery and turning it on only with the power adapter connected. I then reattached the battery and let it charge. Because this only happened twice, I'm not sure this is a solution or just a coincidence.
UPDATE: This workaround stopped working. The laptop was sent to HP for repair yet again. More on this here.