Deleted wrong reply.
I see that the HP Pavilion is sold on ebay is a Desktop HP PC.
Here is HP Support Download page for your HP Pavilion for Windows 7 drivers: https://support.hp.com/us-en/drivers/hp-pavilion-p7-desktop-pc-series/model/5157025
The only thing I can say is you need to contact HP Support or open a thread on HP Forums to see which CPUs are supported by that HP Desktop model.
Depending on your HP Motherboard BIOS and CPU LIST if the Athlon II is supported out of the box or not. That is why you need to contact HP Support or open a thread on HP Forum to see which processor your old HP PC will support out of the box.
It seems like your HP Pavilion comes with Windows 7/8 and a A6-3600 APU processor according to ebay.
The A6-3600 processor uses the same FM1 Socket as the Athlon II X638 processor.
The A6-3600 processor is a APU processor which means it has Integrated Graphics on it so you can connect a monitor to your HP Pavilion Video outputs to get video to your monitor unless it comes with a GPU card then you need to connect the monitor to the GPU Card.
Does your HP Pavilion come with a separate GPU card or not because it seems like it doesn't so you will need to purchase a APU processor to get video to your monitor unless you purchase and install a separate GPU card besides a new CPU.
EDIT: Found this website that shows what CPU is compatible with your HP PC but I don't know how trustworthy the information is. Best to open a HP Forum thread or contact HP Support: https://www.userbenchmark.com/System/HP-p7-1154/5851
