4GB RAM Problem

Solution
G31 chipset cannot remap memory above 4GB at all. All addresses used for devices and video must go somewhere so it is mapped below 4GB.

That's why OEM computers with G31/P31 shipped with the odd 2GB stick + 1GB stick. It was an intentional product segmentation by Intel so they could sell more expensive chipsets, as these are the ONLY Intel chipsets for Core 2 Quad limited to 4GB.
Open task manager, click on the performance tab, and look at your Memory (purple graph) area. I have four GB of RAM and it constantly says 2.4/4.0 GB used when I'm not really doing anything. If yours says X.X/3.0 then one of the sticks of RAM could be faulty? If you have other RAM lying around to test it with I would encourage you to try that and check task manager again for the same info. Also try viewing your RAM in the System window.
 
G31 chipset cannot remap memory above 4GB at all. All addresses used for devices and video must go somewhere so it is mapped below 4GB.

That's why OEM computers with G31/P31 shipped with the odd 2GB stick + 1GB stick. It was an intentional product segmentation by Intel so they could sell more expensive chipsets, as these are the ONLY Intel chipsets for Core 2 Quad limited to 4GB.
 
Solution
Nope.

Next time be more careful when choosing a motherboard. To be fair, no-one in 2007 probably expected it would still be useful in 2017. In the Sunspider benchmark of Java, the difference between 2005's Pentium 4 and 2006's Core 2 is still larger than the difference between Core 2 and today's latest Kaby Lake. Blame AMD for not being competitive for so long, and hope that Ryzen will bring the days of rapid improvement back.