I had a similar problem with mine. The alarm stopped working but the keyless entry and chirping still worked. Well come to find out I put it in valet mode via the ignition switch. On mine if you put in the key and turn it to ON (don't start the engine) and the OFF quickly three times in a row it would activate valet mode. Just do the same thing to take it out of valet mode and back into alarm mode.
Also, if you do find another module in a junk yard, make sure it's the exact same model number. Different models can use different wires in the harness to do different things. Otherwise you might let the smoke out of your wires
Hope this helps you out...
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-2007 F-150 XLT SuperCrew 4x4 5.4L 6.5' Bed
-Bilstein 5100's All The Way Around, Front set at 2" lift
-Gryphon, custom tuned by Bill at PHP
-AirAid CAI
-Flowmaster 3" Cat-Back with 50-series (thinking of changing to a 40-series or a Magnaflow)
-Wig-Wag Headlights and Tail Lights
-Line-X