There are plenty of open-source games out there that aren't very demanding, like OpenArena, SuperTuxKart, or 0 A.D, or ones like Xonotic or Cube 2: Sauerbraten that have nicer graphics and would be a better test of how much improvement an upgrade makes. You could also go the F2P MMO route and try games like Transformice or Pirates, Vikings, and Knights II. What kind of upgrade are you planning?