Hp pavilion dv9628nr notebook just stops running

This sounds like a power problem that I've seen before in Thinkpads (specifically, the x31). Under certain situations, the capacitors will become full and need to be "expressed" (for lack of a better term -- I'm not an electricity guru). Unplug, remove battery, and push the Power button down for about 2-3 seconds, 10 times. Then replace battery and AC, and you should be able to power on.

This can also be caused by something internal causing a non-fatal short in your motherboard, preventing the power-up process. The act of unplugging and removing the battery is enough to dislodge whatever is causing the short, but over time it makes its way back to that annoying place. When is the last time you had your laptop serviced? If it's still under warranty, I suggest a complete cleaning. If it is not, you can download the maintenance manual and either do it yourself, or have someone who has experience with laptops perform it. Trick with laptops is to be VERY detailed about what goes where, and be as gentle as possible. I do not recommend this for the novice who has no expert guidance on-hand.

-J