Was your engine misfiring also? With a broken rocker arm, your valves wouldn't be opening and closing properly clearly affecting engine performance.
I agree that those 3 screws should at least have a locking washer underneath them -- they are very short and small screws that very easily rattle loose, as you found out the hard way.
You said you ran the engine with valve cover off -- did the rocker arms break after you tried this?
~Paul
_________________
'91 300E, 214K miles