I hope that you're not as daft as I am. (I recently spent ages trying to bring my phone to life by pressing the key combination that 'woke it up' without actually pressing the right button to turn it on!).
Try removing the battery and the SIM, then replacing them before pressing and holding the power key (which is the 'end call' key - that's the one I forgot!)
Is that the older slim fliptop one? I've got one of those (which I love) but it does play up and I do what Chris suggested . I have also had to buy a replacement battery which was cheap as chips I think.