adding a new hardrive

It's not that simple,
1) do you have the sata ports?
2) Does your case have 4 free HDD cages?
Again we'll need proper info and pictures to advise.
Let's not wander too much into the APU and processors, can you afford a new mobo? I would open a new thread just for that question and keep this for solving the power and connection issues for the..........4 additional HDD's.

Which HD connections look like yours ?

IDE




SATA

He has a newer AMD A6 CPU, which requires a new motherboard spec, FM2 slot, so of course he has SATA.

OP, run msinfo32.exe from START | search/run box and what is the System Manufacturer and model that is on the System Summary that will appear, please?

Gigabyte what...

You are likely short on SATA cables but need that detail to figure out your port quantity.
[You looked, cheater! ]

I would just buy a 2TB drive, for under $100.

Here is one:

http://www.newegg.com/Product/Produc...82E16822149397

Plus cable:

http://www.newegg.com/Product/Produc...82E16812119269

Otherwise you might be pushing PSU requirements, and you might be already.

Here is a 2TB Seagate in retail box with apparently the cable also:

http://www.newegg.com/Product/Produc...82E16822148910

Lack of power cables, get molex splitters, but again another sign of a less powerful PSU.

OK so you have everything you need with the possible exception of power from the PSU but you can piggyback several adapters together to power the new hard drives. But as mentioned above maybe the best solution would be to get 2 or 3 TB drives or even one of the new 4 TB units?

Totally understand, it sounds like you have the drives and that's more than half the battle. If you can split the power daisy chain into two different psu cables that could be better.