Yes key has a chip. In the Key FOB, or if a no FOB shell type, chip is in the solid plastic of key.
Sound like busted IG SW rod. Replacing rod has no effect on tumbler, key or chip.
FWIW:
Chip is in the FOB, inside master key shell. Remove the back cover screw from master key shell, and FOB pops out. Battery is in the FOB. Battery is for door locks & windows (newer LX). Chip doesn't need the battery. Chip reader is in a ring around IG keyhole.
Why do these rods or keys break:
Some will say, weak design of rod or key, perhaps in part!
But in 20+ years driving 100 series and going back more years in other vehicles with locking steering wheel. I've never busted a key or IG SW.
The number one reason for breaking the IG SW rod or key. Not release steering wheel tension from locking pin. Every time we remove the IG key, steering lock pin sets. If steering wheel is then turned, pressure is then created against the locking pin. The IG key will then, have resistance (not turn easily) as we try to turn. If IG key forceable turned, with this tension on locking pin. Something well break sooner or later.
Typically we don't turn the steering wheel after IG key removed. But, some do with realizing it. By using the steering wheel as a handle, to pull themselves into (or out) the seat. Turning steering wheel, as they do. Why does this create tension on lock pin. As they say: Where the rubber meets the road.