I'd suggest you run "3DMark06" and see what that test runs for you. As long as your FPS don't drop below 20 FPS during that test, you should be able to run the games I listed at pretty good settings. Maybe not at the highest settings, but decent enough!
I have no idea about Borderlands, I haven't checked into that game.
Even my system is showing it's age with the newer games. With computers now a days, my system is at the bottom of the scale for a gaming computer. I can boost mine up there if I overclock it, but I don't like to overclock my hardware. It shortens its life span.
I like to build a new system about every 3 years, but usually do it when prices get cheaper.
I'll check out Borderlands and see what it's about and get back to you.