The new version of the remote app will not run on 3.1.3. Pull the old one out of the trash on your computer, put it back in your iTunes library, delete the app from your phone, then re-install it from iTunes.
The remote requires newer iPhones that are compatible with WiFi remote and Airplay support. Certain features will not be usable as the processing power is not high enough. A4 A5 and A6 processors are currenly compatible with remote.