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No PSU specs? Also, is it a ready-made computer?

All modern computers support DDR3.
Have you thought about a new computer build?

Also I can't find anything about the hp 3032h MobO so it's probably a prebuilt.
What brand and model is your desktop?

You can still buy ddr2, it's a bit costly, but it'll be cheaper than replacing all internals (especially for a prebuilt machine - you'll probably find out that a normal atx mobo won't fit in your box). You can get 2GB*number of ram slots max memory. Typically that means 8GB.

Now that I got the info I need, you can't upgrade the mobo. You gotta get a new computer entirely. I recommend some specs below for you to consider.
Core i5 2.6GHz min
4GB(32 bit)/6-8GB(64 bit) RAM
Nvidia GPU, with at least 1GB Graphic RAM
550-600W PSU, depending on what power level you're using times 2
1TB HDD, with a SSD for the OS if you can afford it
A decent mobo(I won't specify any specific one cause of country differences)
A casing, with USB 3.0 support

And don't get a prebuilt one if you want to upgrade.

don't mind getting mora ram to that pc...
save money and buy a new pc part by part, much cheaper and you get exactly what you want/need.
if you are on a budget go for amd (cpu and gpu). Phenoms are still very good, and the new hd 7770 is a great card for its price.
maybe you can even sell yout current pc to a friend or relative and get some cash for your new rig.