It doesnt play a tune when powering up so you are fine there.
With regards to the phone not vibrating when called, you could try a reset but make sure you sync your data beforehand so you can sync it back afterwards.
I've reset it but the condition is still the same, does this have to be brought to a Nokia service center? The vibration actually works when it's set to vibrate only...is this a defect of the hardware or the OS itself?
That is strange and would indicate the hardware is fine. Are you sure you have vibrate enabled in settings>ringtones+sounds?
Another thing about the vibrate on the windowsphones is unlike the other Nokia's which vibrate continuously along with the ringtone, it vibrates just a few times first and then stops and the ringtone takes over. The two does not happen at the same time and it does not vibrate anymore after those first few times. Maybe this is what you are experiencing.