Is the 701 the 4G version? I have the 2G version. The biggest issue with a distro is size. Most distros these days are slightly larger than 4GB. Have you tried Ubuntu 10.04. I know it's not 100% up to date, but it is supported still.
Maybe puppy linux?
Failing all that, have you thought of Ubuntu Server an then installing XFCE over the top (along with any other essential apps)?
Or you could always install to an SD card...
i5 4440 3.1Ghz, Asus H87M-E motherboard, 8GB DDR3, 2GB DDR5 nVidia card, 2x500GB Seagate hd, Coolermaster 750W PSU running Mint 16 MATE and Win7
eeepc 1015PX, 1.66 Ghz Intel atom processor, 2 GB DDR3, 320 GB hd, Mint 14 MATE. Fan needs fixing.