91 S5 NA Convertible starts but will not idle
 

I have 91 S5 NA Convertible that will only start if I hold the gas down and simply will not idle. I had removed the upper and lower intake manifolds to fix a fuel leak and replaced the upper to lower intake plenum gasket. I took care to make sure that all of the vac lines went back where they were supposed to go.

As I was checking the car, I discovered that there were no sparks going to the lower plugs. It appears that that coil is dead, but how do I know for sure that it's the coil and not the resistor?

Remove the plug wires from the leading coil. Place the plug wires to where they rest against the coil bores. Turn the car over and look for the presence of spark. Also, make sure the coil is bolted to the fender as this is how the unit grounds itself. Which resistor do you speak of?

And what precisely is the idling problem? Too low, too high, bouncing or what?

I used a spark tester and got sparks out of the coil to the top plugs, but nothing from the coil to the bottom plugs. Here is the resistor that I am talking about: http://www.ebay.com/itm/PARTS-1987-M...9ff081&vxp=mtr . It supplies power to the coil (I think)

First off you have an S5 and S5's don't have the item you linked to so it's not a player. Secondly, "And what precisely is the idling problem? Too low, too high, bouncing or what?"
Thirdly, just check for spark in the easiest manner possible which is what I described.

And make sure the leading coil is bolted firmly to the fender and making good contact. Make sure the two wire electrical plug to the coil is connected properly.

Good to know about the resistor thing. It won't idle period. I turn the key and have to hold the gas down before the car will start, and then I have to hold the gas pedal down and keep the RPMs over about 2k or it will stall. I checked the grounding of both coils and even regrounded them to no avail. The plug is connected. I double checked the spark testing and came up with the same results (no spark from the coil to the lower plugs, but plenty of spark from the coil to the upper plugs).

If the Leading coil has no spark then the car tries to run on the trailing coil which makes for a very rough idle. You need to check the plug at the leading coil after you unplug it and the Black/Yellow wire must have 12 volts or so w/key to on. Does yours? Also, the other wire in this same plug, which is Green/Yellow, should have voltage which triggers back and forth from 5 volts to 0 volts w/key to on and the Main Pulley rotated. This wire triggers the coil to fire. If you rotate the alternator pulley w/a socket wrench it will cause the Main Pulley to rotate so w/key to on rotate the alternator pulley a few times while observing the voltage on this Green/Yellow wire and see if the voltage toggles back and forth between the two stated values. The voltage value will stay at mostly one value and then changes only briefly to the other value. Does your G/Y wire behave in such a manner?

And an important question to ask is how long has your car behaved in this manner. Did you recently aquire this car and this is how it always ran or what?

This sounds like my coupe also an s5. Mine does start then just dies. Unless i hold the gas. Once warmed up its better.

Does yours stay running if you hold the gas pedal and how is it when fully warmed up?

I'll have to run that coil check this weekend when I have some time to play with it more.

As far as the last question, I discovered a gas leak under the lower intake several months ago. I haven't started the car until last weekend, when I fixed the leak. Before that, it ran mostly fine, but would randomly run like crap (no power, wouldn't go over about 5k RPMs when floored). I'd turn off and restart the engine, and the problem would go away. Sparks were fine, as well as EGR, and Cat converter.

Sounds like limp mode. You S5 owners should always check for codes when in doubt. Takes but a minute to do.