The rear heater on Suburban has separate heater core in the cargo area, so its independent from the front unit. The front heater core in your Suburban could have a bad heater control valve, clogged heater core, or a bad blend door actuator. If its bad heater control value or clogged core, no hot coolant flows through the core, so no heat. If its bad blend door actuator, the core is heating up, but the blend door to the core is not opening.
In case of AC not cooling everywhere:
- The AC system in your vehicle could be low in refrigerant.
- The compressor is not working due to blown fuse, bad relay, bad clutch, or bad compressor.