I still have my HP Mini311, it has a 11.6" screen, 1366x768, discrete GPU, can decode 1080p in hardware and output on tv via HDMI. In 2009 it was a beast!

I changed the 2.4bg with a 2.4/5n wifi, upgraded to 3GB of ddr3 ram, SSD, overclocked to 2GHz, and installed MX Linux on it, works perfect.