This is a low-cost laptop with a 2nd gen Intel processor. Most low-cost laptops have the processor soldered directly to the motherboard and thus the processor is not replaceable. If it was socketed, considering that I could find no evidence of any versions of this laptop with i3/i5/i7 processors (yet another indicator that it was likely not socketed), this is something that only HP can tell you - if they will even talk to you about a system this old.
I presume you are asking this question because you cannot afford to simply replace this laptop with something more modern. I am sorry to have to say but, considering that it has a 2nd gen processor and is now 12ish years old, it is likely on on the verge of having something major fail within it (heck, even its solder is beyond its MTBF as this point). Trying to upgrade the processor is, to coin a phrase, throwing good money for bad. The money you would spend on this upgrade is money that you won't have to replace the laptop when it does suffer a major failure. I would thus say that you should put up with it as it is until you have the money to replace it completely - if indeed it will even last that long.
Sorry, reality bites,
...S
