My 1st Generation iPod Touch might be jailbroken, but I’m not sure. How can you tell if it is?

Someone stole my iPod Touch, but I got it back. But I hear this clicking sound when entering my pass code and when I open my mail, it notifies me of new mail by playing the alarm sound on the iPods. She deleted all of my data, so I can't really tell. It says I have the software version 3.1.3 (7E18). I also wanted to know that if I restored my iPod to factory settings, would I have to buy the 3.1.3 software again?