Well, the coils arrived from AppliancePartsPro.com yesterday, and I opened the front panel today.

I took some resistance measurement with the multimeter.

First, the coil measurements were as follows, comparing the new coils with the "old" coils that were in the dryer:

Secondary coil - 1250 ohms (new coil), 1200 ohms ("old" coil in dryer)
Booster coil - 550 ohms (new coil), 500 ohms ("old" coil in dryer)
Holding coil - 1400 ohms (new coil) , 1300 ohms ("old" coil in dryer)

It's not obvious to me that the measured resistances indicate a "bad" coil or coil set that was in the dryer, but I guess a coil failure may not necessarily show up in measured resistance? Regardless, I've changed out the coils.

As far as the other components inside the dryer, here's what I found:

igniter - 70 ohms
control thermostat - 0 ohms in power passthru circuit
control thermostat - open circuit between power (red) terminal and motor timer (purple) terminal
control termostat - 7k ohms for interior resistor (to provide extra heat to thermostat during "low" heat auto dry)
sensor at burner - 0 ohms (don't know how to test if this sensor will open as it should when heated, to energize the secondary coil)

QUESTION: do the above measurements indicate any fault with these other existing components? Specifically, does 60 ohms for igniter indicate a bad igniter?

I haven't put the front panel back on to see if the dryer works now. Brian, hopefully you will see this post and perhaps add any comments on if there's anything else I should check/do while the front panel is opened. Thanks.

I've posted photos of the interior components at:
Electrical components inside Frigidaire dryer Photo Gallery by andrew99 at pbase.com

I put the front panel back on and it was a sweet sound when I heard the fire start! I just hope that I did not screw anything up taking the thing apart and putting it back together. So far, tumbling noise and dryer vibration seems normal, and I don't noticed anything unusual.

Some notes on what I learned:

1. apparently, igniter glow is supposed to go off after gas fires up (glow lasts approx. 3 to 5 secs). I guess when the burner sensor opens up, and engages the secondary coil, the resulting voltage drop at the igniter reduces/eliminates the glow. So, the disappearance of the igniter glow after a few seconds would seem to indicate that the sensor at the burner is working properly.

2. Since the old coils had "good" resistance reading, I would hypothesize that perhaps they failed because of a change in inductance due to physical material change of the component. If so, this would indicate that maybe heat from the burner had a long term wear effect on the coil. So maybe (hopefully), I can expect another 10 years from these new coils.

3. I don't know if I did it right, but I had a difficult time removing the front panel from the clips. Finally, I inserted a screw driver into the back of the clip on the left side and pushed forward. And the entire front panel popped off.

4. The other thing that was very difficult for me was inserting the harnesses into the coil terminals. I spent 1/2 hr and still felt that the harness did not "snap" into place. Next time, I should try to slightly file the plastic notch in the coil casing, above the connection terminals. Maybe this would help the notch slide into the key at the wiring harness.

5. Removing the wiring harnesses from the coils were also difficult. I think the coils should be removed from the gas valve solenoids first before trying the connect/disconnect the wiring harness. When trying to remove the wiring harness, next time I would use a small flat head screwdriver to slightly pry the coils from the harness.

6. When removing the front panel, one should have some wood blocks (or other support means) ready, and use them to support the front of the drum after the front panel is removed. Otherwise, I think the weight of the drum may cause too much undue stress on the rear connectors that secure the drum. (In regular operation, the front of the drum rests on the front panel.)

Brian, many thanks for your assistance. I could not have done it without your help!