After re-reading your post, it sounds like your battery is not charging sufficiently, as a result of eroded voltage regulator brushes in your alternator. Even if your battery is almost fully disharged, once you jump start the car, there should be sufficient excess voltage from your alternator to energize the eletrical systems. Sounds like that is not happening with you.
Do your SRS and ABS lights occasionally come on for no reason? Does your dome light blink when you open the door? Does your radio go off when you apply the brakes? Does your rear defroster switch light blink after turning it on? Is your wiper blade slow? Are your dashboard lights dimmer than you remember? These are all symptoms of low voltage. I have experienced them all -- sometimes all at once.
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If you are not getting sufficient power from your alternator, once the car is jump started, and you remove the cables from the vehicle that jumped you, applying any additional load on the battery will cause the car to almost immediately stall.
A key component of your alternator is the voltage regulator, which is simply a set of rotating carbon/graphite brushes that participate in the transfer of electric power from the alternator to your battery/electrical system. These brushes are normally about an inch or so long. As they wear, and become shorter, they become less able to effectively transfer power and need to be replaced.
Fortunately, this is a very easy, quick and inexpensive ($15 to $45) job that you can do yourself. (It is more sensible to replace it when the engine is cool, since the alternator is so close to the exhaust manifolds on the 260E.)
You simply unscrew the existing voltage regulator from the back of the alternator, and replace it with a new one. That's it. This is where they are (in Fast Lane) and what they look like (click the small photo for an enlarged view):
http://catalog.eautopartscatalog.com/mercedesshop/wizard.jsp?partner=mercedesshop&year=1989&make=MB&model=260-E-001&category=All&part=Voltage+Regulator
Check yours first to make sure the brushes are worn. The alternator is on the passenger side of the engine, in plain view. It is the squat cylindrical device connected to the lowest pulley on that side of the car. The regulator is attached to the back of it with two screws. Remove those and pull it out.
If the brushes are much shorter than what you see in the photo, then the voltage regulator is the culprit. If, however, the brushes look fine, check your serpentine belt tension and condition. If it is too loose, or excessively oily, it will not spin the various pulleys -- including the alternator's -- at the proper speed, which will also cause a no-charge condition.
The stormy, windy, wet conditions you describe are enough to make a loose or oily belt slip cheerfully over the pulleys -- sometimes accompanied by the most delightful chirping sounds. :p . The water pump, power steering, and alternator pulleys are particularly vulnerable. By chance, was your engine running hotter that night? Was your steering a bit heavier? (I'll wager that you were running with your fog lights on as well, further draining the battery.)
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If you feel, however, the ignition coil is the problem, it is bolted to the ABS pump on the driver's side of the engine, next to, and somewhat below, the power steering fluid reservoir. It is covered by a black plastic, kind of teardrop shaped cover that lifts right off.
I have never replaced a coil but I imagine it is essentially a bolt-on job, requiring only the unscrewing then reattaching of two wires from the battery, and unplugging and replugging the one heavy ignition wire to distributor.