my HP510 powers off. Why?

Hi,

I  have been using a HP 510 for several years.

Product Number : RU964AA
Description : HP 510 NOTEBOOK PC,

As OS, I have WinXP and Fedora17 (mostly I use Linux).

In the last couple of weeks, it suddenly powers off. More precisely:

-- if machine has been not used for a couple of days, it powers off when booting. After I try several times (with battery removed)  it boots fine and works for hours;

-- at random, it just powers off. After that, it boots fine, usually at my first try.

I suspect something on the adpater, or .... ? Your advise in welcome.

Also, I would like to buy the following two parts

(which I understand are apt for my machine, are they?)

440704-001      Battery (Primary) - 4-cell lithium-ion (Li-Ion),
14.4VDC, 2.2Ah, 32Wh     
        
613149-001      AC adapter (65 watt) - Input voltage 110-240VAC,
50-60Hz, 2.4A, 19.5VDC output voltage, nPFC - and a the separate 3-wire AC power
cord with C5 connector

I am in Italy, and I do not see how to buy them from HP on line from here.

Your helpis welcome

thanks

regards

mario