I searched this topic on this website already and I saw that the memory stored in the GPU or whatever will have no affect on the motherboard in terms of compatibility. But, I contacted HP and asked them the same question and they responded saying this:
Firstly I would like to thank you for forwarding me your query and giving me a chance to assist you with the issue.
I would like to inform you that the HP Pavilion a6614f Desktop PC does not support DDR3 type graphic cards. As the computer does not support DDR3 type memory. The computer is having 1 PCI express x16 slot. This slot is used for adding graphic card. You can go ahead and add PCI express x16 type graphic card. The motherboard will support ATI graphic card, brand doesn’t matter but it should be PCI Express x16 type card.
Does this guy know what hes talking about or not?. As of now, I don't know what to do.
Sounds like you talked with the Bahgladesh section at HP. If your MB accepts a PCI-E graphics card, the DDR3 is fine as long as your PSU is sufficient. According to your HP specs, you have a 300w PSU and the GPU specs on Newegg state that 400w is needed for that card.