My car horn continuously goes off in 2004 Grand Am

How are you 'locking it' to make the noise?

clock spring connection and is a known issue.

https://www.google.com/search?q=2004+pontiac+grand+am+horn+not+working

What does 'cruise control' have to do with the horn not working?

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Something going on with bcm. Note the diagram for the horn, one of the ground wires for control side of horn relay, goes to bcm. Probably part of security system. The other ground wire goes to horn button.
The bcm also has control over door locks. I can't diagnose your bcm from here.

have dealer check sensors do not continue daily driving!

if you have a power distribution box there is a cable that goes to it that could be corroded and it is not letting voltage through is there power to anything like the horn lights stereo

PJB?

soft material on horn buttons shrinks in the cold causing horn contact

Normally if a horn operates the horn is good. If it blows continually then it is the horn switch on the steering wheel.

Sorry, it is easier to replace the horn than the switch.

get assistant to hold horn on then tap it with a hammer and see if it will work ,often works

no, sounds like its time for new horns, have someone push horn button while you check for power at the horn, if theres power then replace the horns,sounds like bad horns to me,good luck.

IF horn is going off then it is not your horn.
most likely your horn pad switch sticking this requires airbag to be removed to replace.
if it is going off and lights flashing then you may have a security issue