the COM.GSM can only operate with 2G networks. Are you sure in your region 2G is still operational? The fact that the SIMs work in a smartphone doesn't automatically mean they work in the COM.GSM as the smartphone could connect using something else than 2G.
That said you can try the following command. This will tell you if the modem has registered with a provider.
+COPS=0 // auto mode not registered
+COPS=1 // manual mode not registered
+COPS: 0,0,"CHINA MOBILE" // auto mode registered
Or try to get a list of available providers.
Note: this command can take a long time and sometimes you need to issue it multiple times to get a result.