Well, you apparently don't have LTE either. And if it displays 4G that means you have a cellular signal; if you didn't it would display "No Service." Who is your carrier? Most carriers call LTE "4G." The exception is AT&T, who calls GSM HSPA+ "4G" (although it isn't). Either there's a problem with your account or you have roaming turned off and you are in the area of a partner carrier of your primary carrier.
Text does not work on WiFi; it only works on cellular voice (iMessage can use WiFi, but not SMS).