Are you still using the factory radio? There is a diversity antenna that is printed onto the rear window as part of the rear defogger grid.
Patent US6239758 - Vehicle window antenna system
There is also an antenna amplifier module. Check for 12 volts and ground.
AM needs more of an antenna than FM, so you may have little or no AM reception if there is an antenna problem.
First make sure that everything is plugged in and there are no pinched wires. A 3' long piece of wire can be used as a substitute or test antenna in the back of the radio to make sure that it is an antenna problem and not a radio problem.
Very much so. I did radio/microwave in the Army and have some antenna knowledge. Was working for the local Cadillac/Olds/Nissan dealer in 1970 when GM switched to windshield antennas. On of the first "assignments" I was given was to reinstall the radio in a 98 that had been on the lot unsaleable for 3 months because the radio wouldn't work. They had sent the radio out for repair three times and each time when it came back it wouldn't work, so they sent it back. Problem, of course, was the antenna. The lead was pulled loose at the base of the windshield under the dash where it wasn't visible. None of the mechanics in the place had any clue about radio and didn't know to stick a test lead into the antenna socket on the radio to see if it would then work. So it went to the body shop for a new windshield.
I had two GM vehicles from the late 70's ('79 Monza and '79 El Camino). As I recall both had the embedded antenna's. They were okay as I never had reception problems. Both were equipped with AM radio only (ugh!). I added a FM converter to the Monza. It worked quite well for a $15 unit.Early (1970s-80s) GM had horrible problems with the embedded windshield antennas. They were directional, they were affected by wiper operation and as noted, if the connector wires broke at the base of the windshield, they were awful to repair.
Nowadays, these printed (not embedded in the glass) are much better and many automakers are using them.
Radio gain/noise rejection circuitry has also improved vastly since the 1970s.