You have a good case. But I think the time elepsed will go against you. I would think it is worth the battle though.
Here is a page which clearly shows the CPU you have , MK-36, is single core.
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It is a tough situation, but, browsing around, I can see that at some stage HP modified the socket to 754, which would accomodate your CPU or the new TL-52. I am only guessing, but it seems that you have a motherboard whic can handle the more advanced CPU but still has the single core.
Sorry M8, but good luck. Perhaps, worst case, you could do a deal with the seller for an update.