Hi Maryannd,
I have an iPhone 6Plus, and used to have an iPhone 5. My Mother had an iPhone 3GS, and now uses a different iPhone 5 to the one I had. They ALL had the same problem with the phone only vibrating when it was 'ringing', when do not disturb was OFF, and the ringer volume on MAXIMUM. The only 'switch' or button on the iPhone that can cause this, is the little switch at the top LEFT corner of the phone when looking at the screen. I am not sure but I think on iPhones older than iPhone 6 that this switch could be set to either 'mute' the phone - therefore it will NOT make a noise, but just vibrate instead when a call is being RECEIVED - or you could set this switch to 'lock' the screen instead (although I think a better screen lock would be with a passcode, being more secure from unwanted attention).
If the button you describe as the 'silence' button is the same one, then this button is 'activated' when you can see the 'coloured part' (orange on iPhone 5 and 6Plus) when the switched is slid forwards towards the front of the phone and obviously DEactivatedwhen slid backwards. If there is some 'other' setting on your iPhone 4 that does the same or similar thing I am not aware of it, since I have never used an iPhone older than an iPhone 5.
I hope this helps. If it does not, then try an Apple Store Genius Bar Appointment, or (if you are in the UK, you could phone 08001076285 for Applecare Tech Support, but be prepared for people who leave you on hold for ages, don't know the answers, and sometimes cut you off when putting you on hold (while they are 'getting the answers') and DON'T phone you back when you are cut off, even though the first thing they ask you for is your phone number so they can 'ring you straight back if you get cut off!!!'
Good Luck
Bob