Two thing to try. (and I'm the owner of a very busy cell phone repair shop, and this is what we would do if you came in with the same issue).
1. Take the public sim and try in another phone that you know works and is unlocked (or locked to Telus). If the sim works fine in that phone...then you know the sim is fine.
2. Take another known working sim (from any network) and try it in your new phone. If the known working sim doesn't work in your phone, then you know the issue is with your phone specifically. If the issue IS with your phone, then you need to contact the seller and either try and return the phone, or get them to show you the phone is working with their sim.
A damaged sim reader in a phone can cause some Wonky things to happen, but if phone isn't blacklisted (or grey-listed....and yes, there is such a thing....locked by a network for non payment of contract), and doesn't work with 2 different sims, then the phone is the issue.
Hope this helps.
Jason
