Is it a factory alarm ? (I don't know whether or not the '89 W124 had that)
but the first thing to do is open the door, release the hood latch, open the hood and take out the appropriate fuse, (your owner's manual should point to which one that is)

I think the fuse box is in front of the firewall, left side(?) but not sure...

If it is one of those aftermarket car alarms, that's another matter, most of them are well made but when the installers are done with them, it was like they got put in by monkeys at midnight

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1991 560 SEC AMG, 199k <---- 300 hp 10:1 ECE euro HV ...

1995 E 420, 170k "The Red Plum" (sold)

2015 BMW 535i xdrive awd Stage 1 DINAN, 6k, <----364 hp

1967 Mercury Cougar, 49k

2013 Jaguar XF, 20k <----340 hp Supercharged, All Wheel Drive (sold)