when you say it keeps running- do you mean normally or is it "running on" or dieseling? if it's dieseling, the quickest way to flush carbon is a water tune up. (2500 rpm, drizzle (SLOWLY!) a cup of water down the carb and have it burst to steam blowing the carbon out). Seafoam in a vacuum line can do about the same.

if it's truely staying running NORMALLY with the key off, then it's electrical. the fix (if the key cyl is good) involve putting a diode inbetween the alt and the ignition (on some cars- i dont know yours well) this keeps the ignition from being backfed. -been awhile since i had to do that so i may not have the details acurate.