Is your computer similar to this one? http://reviews.cnet.com/HP_Pavilion_a1230n_Athlon_64_3700_2_2_GHz/4507-3118_7-31518258.html?tag=sub
If so, the only question that really needs to be answered is the BIOS update, which may be needed to support the higher end processor. Receiving this information directly from HP would be the best avenue for confident upgrading.
Assuming you have an available 'PCI-express' slot like the linked machine does, then the video upgrade would probably entail the purchase of a power supply (minimum 350 watts, 400+ recommended).
Note - you will want to check the available space between the rear panel and the front drive cage inside the case to verify that the card will fit length-wise in the case.
The memory should not be a problem.
As a side note, the ASUS board is certainly built for the OEM market, and therefore ASUS may not be willing to provide any support.
One other option is to upgrade the same size ASUS motherboard for fairly cheap (which supports the processor you want) and you can remove the question on the BIOS and support completely. I believe the board you have is in the 'Micro-ATX' form factor. Here is one example of a good board by ASUS http://www.newegg.com/Product/Product.asp?Item=N82E16813131040
Others may have better ideas.