The error on the Asus E1000H was a strange one and the solution equally strange. On startup one or more programs e.g. GoogleUpdate.exe would report "The application or DLL C:\WINDOWS\system32\dbghelp.dll is not a valid Windows image. Please check this against your installation diskette" which does helpfully point you at the problem.
The fix was simple, I copied the file dbghelp.dll from a working Asus E1000H and overwrote the corrupt one. It is possible that simply copying it somewhere else and copying it back would have worked but that's not what I did. An alternative fix could have been to use system restore, had that been available.
So how did the problem arise? I'm not sure but it seemed to coincide with the netbook running out of disk space, so perhaps that caused some kind of corruption of this file.