When i start my 96 mustang gt the horn is blowing

probably damaged/ burnt up battery test battery

I looked your security system, it said starter motor disable. It will probably also disable your fuel injectors. If security system has a problem, you may need a scanner that can communicate with your security system. Also, sometimes when battery voltage is lost, some modules may need to be reprogrammed. Are there any applicable trouble codes?
You can check the basics, spark at the plugs, proper fuel pressure, compression.

lightly?seems not...
does it crank robustly or not?
no car starts ,if cranking dies
un less my car, push started or gavity started.
check fuse first. read how to do that? using meter?
then check battery voltage , 12.6v rested.
of ok and lugs clean there
then turn key to on
does the cluster CEL lamp glow, if not fuses did blow.
ok now crank,, does it crank fast?
yes/no>?

i once was rear ended with fast sally mustang (texting sure)
huge plastic front end, on this car, 50mph hit
me, not so good
her car looked ok, the plastic bs popped back looking ok!
but if you pop the hood, it was wreck inside. as expected.
so lightly has degrees, as does all damage.

if its a handchiffted gearbox put in highest gear.
puch the car to the front and back till you hear a click.
if he starts .check the ignition.if this is not correct the car have a death spot.

since its a 12 bring back to dealer have them reset program -some of the problems can be --weak battery in fob----if their is a problem that sets off a check engine----battery went dead -----program hiccup but vehicle should be under warranty

check for water damage on the computer. it sound like a mustang i fixed a few months ago. the customer broke the windshield and the body control computer got wet. so the car was cranking itself or turning lights on when raining until running battery out of charge. he could not drive vehicle on rainy days until 2 or 3 days later. this car wasn t convertible but since u said they change the winshield i could be leaking water.

94 was a new model freshening and I have 94. may be similar.

Horn Relay and fuse is in fuse box in engine compartment, driver side in front of strut tower.

Horn System The horn system includes:

• Dual horns (13832) (one high pitched, one low pitched).
• Horn blow switch (13A875) which grounds the horn relay, which energizes the horns .

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check to see if all of your cables are intact and nothing is grounding out anywhere

Ford horns are famous for this disconnect the black ground wire from the horn front of vehicle next to radiator. This will stop it for noe you will need to replace the horn all the parts houses have them. Good Luck

check freon in system if not enough freon compressor wont kick in