From your old computer specs, you will have to upgrade RAM as well: You need DDR3 for those Motherboards you listed.

I will need the specifics of each part that you already have

• GPU - What is the slot size or just the name of it
  
• New Power supply wattage
  
• Heatsink - Socket type: 775
  
• Tower (Case) Size - Mid-size ATX
  

Do you plan on getting a new case? HP and Dell cases suck

You have a SATA HDD. All newer MOBOs come with SATA. As long as the MOBO it isn't IDE, we're good. With that said, you surely can boot and keep all files.

The only thing we need to look at when comparing MOBO to CPU and making sure those two are compatible is the socket size/type. Overall, making sure the case size can fit the motherboard would be key. In this case we're good as well.

Unfortunately I don't believe your current heatsink will be compatible, but of the links you listed, I would go with:
http://www.ebay.com/itm/NEW-AMD-A6-5400K...51a44f8d5f