The ignition barrel turns a cam in the steering lock. That cam does two things. It locks & unlocks the steering wheel, and it's also what turns the ignition switch. That cam (or link as Jeff called it) is cast out of some crap metal. That's what breaks in the steering lock usually rendering the wheel unlockable and the car won't start since the ingition switch isn't getting turned over with the key.
Pull your barrel out again and take a large flat bladed screwdriver and try turning that cam with the screwdriver. It should be pretty obvious where to put it when you look at the butt of the barrel and the part it interfaces with inside the steering lock.
If you can't turn that cam (or it just turns freely) then your steering lock is broke.
If that turns with some resistance then stops (like it would if you were normally turning the key over) then you should take your ignition switch off of the steering lock and see if that turns like it's supposed to or if it's broken and froze up.
Ignition switch is easy to replace and was around $100 if I recall right.
Steering lock was around $150 and was a bit of a bitch to replace. Involves removal of the steering wheel, removing a pair of anti-tamper bolts (by cutting a slot into the top of them or using a cold chisel to start backing them out), and taking a pair of snap ring pliers to the snap ring on the steering column to pull the steering lock assembly off the car.
Cosmos Black/Black 1995 540iA M-Sport
BMW Individual Exclusive Edition, 1 of 65 total, 9/25/95 Build