Damien, you're right about the importance of culture. A main thing also often overseen is the absence of nationalism before (roughly) the 18th century. So cultural and religious differences were often much more important than ethnic differences. Take the 30 year war as an example.
But to say the Prussians were not Germans is nonsense anyway. Prussia in the 19th century was a German state, nothing else. It was part (and even one of the leaders) of the "Deutscher Bund" (German Federation) at that time. After the 1866 war with Austria Prussia became the hegemonial power in Germany leading to the Second Empire, which now was based on nationalism.
In fact for many decades (maybe even until today) many things considered to be "German" were (are) originally Prussian, for example militarism.
Anyway, back to the Holy Roman Empire. As far as I know the period from 962-1806 is considered to be the Holy Roman Empire in it's closer sense. It was 'founded' by the German king Otto and the Pope (I think John XII). Its predecessor was Charlemagnes(Charles the Great's) "Roman Empire" from 800-925. Some see the whole period from 800-1806 as one, for example those who argumented in favour of another "Thousand Year Empire"
