If, when you put the sim card in, it does not ask for an unlock code, then it should be unlocked, so i'm not sure why you you think that seems to be the problem. When you go into settings, mobile networks, available networks you can try the "Search Networks" option, or you can try select automatically.
Also I did a quick look on the g3 at the site the other poster referenced. Not being sure of the exact phone you have I sorta winged it, but it looks like the phone *should* be available. The caveat here being that compatibility hinges on what network your phone was on originally so what frequencies are available. Some of t he models would work on 2g or 3g but not 4g. So you can try going to mobile networks again and check out the "Network mode" setting, and see what's selected then try some of the other options..