Debian on old or slow computern
Consider using OldStable or Stable. Add Backports to your repos to get more software.
Replace websites with special software
Use youtube-dl -f fmt (e.g. 36) to download videos from Youtube and play it with mplayer or vlc. The english Wikipedia article has a list of supported formats.
If your computer is too slow for iceweasel showing OpenStreetMap, try foxtrotgps.
xbmc or xbmc-standalone (xbmc with X but without a window manager) with radio, youtube or Mediathek plugin may or may not be useful for old computers (xbmc requires 24bit colors).