My vehicle engine continues to operate after turning off the key

What is your question?

When turning the key off on my vehicle, the engine continues to operate/run; even if the key is taken out. The only way for the engine to stop is to either take off the battery cable and unplug the alternator or if I take out the automatic shut-off relay plug from the fuse box under the hood.

What makes this problem better or worse?

Not sure

How long has your 2004 Dodge Durango had this problem?

Several days