First thing to check is the power supply to the radio.
A transceiver uses much more power to transmit than to receive. If the source of power is (current) limited, then the set may well receive perfectly but "fall over" when trying to transmit.
I don't know the Garmin. Does it use its own on board batteries, or external power? If it uses its own batteries, are they a make with decent performance e.g. Duracell professional.
If it uses external power, get a multimeter and check the voltage feeding the set. If that is healthy, then if you can, check the voltage when the set is transmitting and see if the voltage drops significantly.
The loud buzz: was that with the aircraft engine running? A buzz suggests power supply faults, alternator problems, or possibly earthing faults/ miswiring.
If the power supply is good, then the set transmit might be faulty. The transmitter could have failed and only working at very low power - giving a very short range. When you said you had strength 5; was that reported by the tower? Is it a new set or one you have used successfully before?