According to the specs, the HP Pavilion p6823w Desktop Computer was introduced for sale on 27-May-2011 and shipped with Windows 7 SP1 64-bit. All this talk about Vista, makes me think you are referring to a different model.
If it is indeed a HP p6823w that went bad, you can find the "N-Alvorix-RS880-uATX (Alvorix) motherboard" out there on the internet. There appear to be a couple of revisions but I don't know what the differences are. Also, you would need to have the board "Tattooed" by HP or an authorized service center to put your computer's infomation on the motherboard. If this isn't done, then the HP Recovery Discs won't work.
If you go with a board from the previous AM3+ list, the AMD 760G chipsets may be close enough for Windows not to crap out. The AMD 880G chipsets may also be close enough. In both cases, you will need to purchase a new copy of Windows and may need to reinstall everything from scratch.
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