I believe you mean 1 TB storage (HDD), not memory - correct?
Your question is still wide open as there are many things to consider.
Here is a link from within this Forum that will help you move forward if indeed you decide to do so.
http://www.tomshardware.com/answers/id-3574837/latest-motherboard-suits-pentium-processor-ddr3-ram-type.html
Then google "motherboards for intel pentium (r) dual core processor 3.1 GHz"
Look at the products available and the prices. Select two or three motherboards that meet your budget and then take a careful look at their specifications. Read reviews and look for the motherboard installation guides/manuals. Learn as much as you can about the choices available.
Ensure that the motherboards will indeed support the CPU along with whatever else is to be installed in the case. It all must fit; especially the motherboard into the case (CPU cabinet).
Would not recommend a HDD - a small (256 GB) SSD may be more viable and could be used elsewhere in the future.
And what wattage is that PSU? How old is the PSU and in what condition?