The problem probably isn’t fuel injectors BUT try adding 4 ounces of Chevron Techron to a tank of gas and riding 75-miles. Techron is magic. This might be all you need.
I just scanned the conversations and may have missed this part of the discussion: pulling plug wires on conventional coils while the bike is running is not good; the coil can be destroyed. The coil should be grounded before starting the bike. It was not clear if the lower plugs or the power to the coils buried in the frame of the S were pulled. Removing power to the coil is the best way to check to see if a plug is firing. ‘04-on 1100S’ have two, lower plug-coils, one for each lower plug so isolating an individual plug is possible.
The original center coils on 1100S twin sparks failed with regularity. The original, single spark to the center plug was a conventional, coil mounted on the bike’s frame sending high energy to the center-mounted plug. On twin sparks, the center plug’s coil is in the cap that attaches to the directly to the plug’s tip.
I went through six (twin spark) coils before BMW issued a superseded coil-fix. I currently have more than 140,000 miles on the superseded coils with no failures.
The other end of the coil (the spark plug end) is where the large voltage across the spark plug’s gap discharges.
Uncapping the plug downstream of the coil while running takes away the designed-in grounding (jumping from the spark plug’s center electrode to the plug’s grounded electrode(s). The stick coil will be damaged if pulled from the spark plug while running. You might get a nasty shock too if the hot coil grounds through you.
However the stick-coil-in-plug coil’s low energy wire can be pulled while the bike is running because as its name states; it is low voltage. Disconnecting here stops the energizing of the downstream coil.
This is where the center coil’s health should be checked. It’s very easy to do with the engine running at idle. The black plastic “Twin Spark” cover is a friction fit and pops off easily. On BCR’s the CF valve cover protector must be removed first.
Once the cover is removed the low energy lead can be slipped rearward off the coil by carefully lifting the tab securing it to the coil. If the coil is functioning the idle will drop 25 rpm. If no rpm drop is had the stick coil is bad. If the engine dies, the opposite stick coil is probably bad and the bike is attempting to run on only the lower, conventional coils/plugs.
The idle can be set artificially high masking a bad coil. It might even be possible to mask two failed coils but I’ve never tried it.
The center coil-test should be done for each side. Again a 25 rpm drop per side shows the center coils to be good.
Two photos attached showing example of “good” and “bad” coil part numbers. The manufacture date “/09” and “/11” are the superseded part numbers. The “/03” is original failure-prone” part number.
Again, the original coils fail around 20,000 miles so it doesn’t matter how old the bike is; it’s mileage driven. At 40,000 miles an S could be on its second set of (failed) old coils. My ‘04’s fifth coil failed at 40,000 miles in late 2009. I believe this is the first year of manufacture of the superseded coils. The sixth old coil failed in 2011.
The apparent date-of-manufacture discrepancy (‘09 and ‘11) is due to my moving coils to each new-to-me 1100; one-‘04 1100S and two low mileage, ‘04 BCRs (10,000 and 2,500 miles respectively). The coils hadn’t had time to fail. When I sold each 1100, I told the new owners I had done this and to expect failures. The old coils failed like clockwork.
Once the coils are determined to be good or have been replaced (make sure of the mfg. date if buying used or NOS), then check the idle and TB sync. It was mentioned that a TB throttle plate bushing could be worn allowing unmetered airflow. I don’t think your bike has enough miles to be suffering from this. A cracked, missing or leaking charcoal canister hose from canister to TB could also cause unmetered airflow which causes erratic idling.
The quadrant that rotates the throttle plate when pulled by the throttle cable can be hand-shaken at idle and if it is in-leaking air the idle will change.
DO THE FOLLOWING OUTDOORS AND HAVE A FIRE EXTINGUISHER READY AND KNOW HOW TO USE IT BEFORE TRYING THIS:
Spraying propane at the TB-area, including the charcoal canister hose attachments (or TB-caps if the canister has been removed) will also identify an unmetered air leak. Don’t use starting fluid, brake cleaner or any other liquid mist as the liquid may permanently stain the TBs.
The idle will increase if a suction-leak is present.