Right…so if anybody else in the world is wondering, it appears as though the 32bit version of Ubuntu Desktop 10.04 will disable networking following a hibernate.
It does not matter whether the system actually manages to restore from the hibernate (mine actually crashed), nor how many times you power it down and restart it.
$ sudo service networking start will not fix it either.
To fix it you have to use the mouse, right click on the network connection icon in the top left hand corner, and choose “Enable Networking”. WTF?