iPhone will charge but won't connect with iTunes or iPhoto

I have an iPhone 5 and a Mac OS X Version 10.6.8

When I connect my phone to my mac, the phone makes a noise to say it's connected and begins charging, and asks me if I trust the computer. However, when I load iTunes on the computer, nothing happens to say the phone has connected. When I open iPhoto, the phone flashes up in the sidebar as if it's about to begin importing photos, but then disappears, then re-appears, and so on, but won't actually connect.

I have tried:

• Switching off and on again on both devices
• Using both USB ports
• Using a different iPhone cable
• Updating my computer software
• Logging into my computer in safe mode
• Getting rid of any security software or add-ons on my laptop

Nothing I could find on any help forums has worked. I bought my iPhone on eBay as a refurbished model. Could that have something to do with the problem?

I don't have any Apple care cover, and I can't download any of my photos or put any music onto my phone so it's a real problem.

Any advice you could offer would be gratefully received.

Thank you