Postgres develops server doesn't listen error spontaniously
This problem was resolved with the following actions:

Postgres 9.3. was uninstalled

Postgres was re-installed with a different data directory

The postgresql-x64-9.3 service was now running.

I stopped postgresql-x64-9.3

Then I cleaned out all the folders in the new data directory (I kept the new config files, in case they were the source of my problem).

I copied across my old data directory files (as per https://stackoverflow.com/questions/3305961/recover-postgresql-databases-from-raw-physical-files)

I restarted postgresql-x64-9.3

The old databases were now working

Thanks everyone for your suggestions