The most popular way to fix a "bricked" iPhone or iPod Touch is by putting it into DFU mode. This is tricky, but it will solve that pesky stuck Apple logo on boot.
To do this you need to turn your device off. When it is completely off, push and hold the power button. Count to 5 and then push and hold the home button (keeping the power button pressed down still). Count to 10 and then let go of the power button (keeping the home button pressed down). Count to 30 and you should hear some notification that the device has been put into DFU mode. Now you can restore it in iTunes.