I can run most distros on a 2GB machine with a 1.2GHz dual core processor, the 'heavy' desktops like KDE & Gnome will be slow, but I tend to use XFCE desktop, else a lightweight Window Manager, such as JWM, IceWM, Fluxbox, etc.
Try running a few 'live' distros that you like from pendrives, or...