I'll purchase a Gigabyte GA-B75M-HD3 motherboard for my i3 3220 but I don't have the extra money atm to buy new Ram, so can I use some old 800Mhz 2gb DDR3 ram sticks(2x) on this motherboard even if the specification says it supports 1600/1333/1066 MHz memory modules?
You can use those modules probably. Put them in your ram slots and if the system reaches post screen go to bios and increase the timings. Since you cannot set the ram frequency below 1066MHz, the ram will run in the over locked stage.
It is highly recommended that you but a ram card even 2gB for now.
Even though it says it doesnot support that card, there is a good chance that the 800MHz card can get your system running. So when you plug the card it will automatically overclock it to 1066MHz. You cannot decrease the frequency but you can increase the timings of the ram to make the card more stable. Just make sure that the voltage is correctly set in the bios.
You can try this out even if it doesnot work it won't damage your motherboard or other components. It is always better to buy new ram cards.