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I have three (Pentium M) laptops. They are all in a good physical state and work perfectly well, so I have no reason to stop using them When I first attempted to update to 12.04 the installation failed, reporting that the processor did not support pae. This led me to ask the original version of this question. This did not solve my problem, the question was marked as 'asked before' and not answered. None of the 'asked before' answers solved my problem so I was left with laptops I could not update.
As I can't actually add my own answer to this question due to it being labelled as 'asked before' (even though this variation of the pae question had not been asked), so I will answer it by editing the question.
I did some research on the Pentium M and discovered that it DOES in fact support pae despite the installation not finding it. The solution to my problem was to use the 'forcepae' boot option. From 14.04 onwards I believe this problem has been fixed in the installation.