Hello Matty,
i had the same problem as you and i´m having it again.
MacPro 2008 with 4 Gbytes and 2 harddrives.
After one year of use i started having problems like you, randomly when i pressed the power button: lights on, chime and nothing....no apple logo. This symptom increased until i couldn't start the computer any more. The computer presented also the same sympthon as Hitcher. Sometimes i couldn't startup the computer for hours, or days....
My computer was at repair center almost 6 months !!!! For them, the computer was alright until i was lucky to show them that the computer was not ok. So, they replaced the PSU....and it was ok, for 15 days.... then.... it started with the same sympthons..... crazy!!! but the repair center wouldn't make the repair again because it was out of guarantee (6 months in the repair center..!! time goes by...in Europe we have 2 years).... After almost 6 months i was able to convince Apple that my computer was out of guarantee because of the time it was in repair center. I took my computer to another repair center and they replace the PSU...
I´m working with the computer now for one year since the replacement and it started again.... so... i believe that i need another PSU... very strange issue.... this is the third PSU to be damage
PS: my graphics also was replaced....but it was the model with problems that apple had a replace program .... althought again... i was not lucky... they didn't accept my card... the replace program had terminated!!!