Ok, I will try and tie a few things together here. My car is a sedan, and the antenna is definitely in the glass. The reception is weak on all stations, even ones I know that normally get good reception in my area. I will try to get access to the coax at the back of the radio, and I assume there is another coax connection at the back glass. I will wring it out with a multimeter and make sure there is good continuity. If it is not good, does anybody know the run of the coax? My intuitive thought is that it goes behind the front passenger kick panel and through the right side rocker panels to the trunk. The reply from "off-track" (above) leads me to believe there may be a connection behind the kick panel as well. This will take some time, but I will post my findings afterward. It may be a few weeks, though.
There's an antenna amplifier under the headliner. According to my factory manual, the "Antenna Amplifier Module" is located "Right rear of the roof, under the headliner".
So the wire from the rear window grid goes to this amplifier. From this amp, the coax goes to the radio. There's also a pink wire from the radio which supplies power to this amp.
I'm not sure of the routing. If I can find it in my manual, I'll post back. For now, my best guess is the coax goes down the C-pillar on the passenger side, then behind the rear seat ahead of the passenger side wheel well, then under the carpet towards the front, coming up behind the carpet in the area between the radio and glove box.
In my experience, the contacts on the grid on the rear window break loose. Inspect the window and check the wires. I think there should be 3. Two are usually about halfway up, one each side of the window, supplying power and return for the defogger. The third wire is usually up high on the glass, connected to a separate grid near the top of the glass that functions as the antenna.
If the wire is broken from the glass, you can get a repair kit at parts stores. It uses conductive epoxy for gluing the contact back onto the window.
If the antenna is connected to the amp, the next thing to check is to see if you have power and ground at the amp. With the radio on, check to see that you have 12V on the pink wire at the amp. Also check that the amp is connected to ground - that its ground connection has not come loose or become broken.
My thinking is that your weak reception is either a broken connection from the grid to the amp, or no power to the amp.
If you need to trace the antenna from the amp to the radio, it's a bit of a pain, but not too awful - it's not a heater core
You'll need to remove the rear seat, and the front passenger seat, along with the trim along the rockers. But follow the wire, and only remove what you need to as you go from back to front.
But before you do that, pull the head unit and inspect the antenna connection there as well. That is, look in the obvious spots first, then start the tedious part of removing seats, trim and floor coverings.