'96 328 intermittent shutoff

[Brian Olsen]

I own a '96 328i, which is exhibiting the following intermittent
problem(s). I would really appreciate any light you can shed on the
subject:

1) Sometimes, when the key is inserted in the ignition and turned, it
will merely spin in the tumbler. The lock will not engage, and the key
will continue to rotate for greater than a full revolution.

2) Sometimes, the key will engage the lock, and the lights, instruments,
etc. will come on as normal. However, the starter does not turn the
engine over. Nothing. After a few turns in the tumbler, the car will
start normally.

3) Most troubling is that sometimes, while driving, the engine will
suddenly cut out. The cutout is sudden, total, and (so far), lasts for
only a second or so. The engine will then restart, and continue as
normal.

Otherwise, the car runs perfectly. The combination of symptoms above
tends to rule out the starter, coils, battery, etc as the source of the
problem. The only thing I can think is that it is related to the
security system, and the chip in the key, and/or the mechanical or
electrical portion of the ignition switch. I notice the key has no
battery to power the chip inside, and conclude therefore that the key
completes a circuit, and the chip receives some small voltage via the
ignition (tumbler) itself. The key is somewhat loose in the tumbler, and
I imagine that if the circuit is not complete, the security system will
not receive the required code from the key, and will act to immobilize
the car. So far, I have cleaned both keys up, and removed any other keys
from the key ring (i.e. no extra weight on the ignition key).
Does this seem plausible? Anybody BTDT? If so, would you care to
enlighten me as to remedial actions, costs, etc.?

Thanks.