get it to not work and check it out. could be something as simple as a bad ground on the siren (should be barried under the hood somewhere). the wire from the brain to the siren is often brown. this wire connects to the red siren wire. a red/blk wire should be ground (these colors are common, but not always the case). the brown wire should show constant 12 volts when the alarm is set off. also check the siren (hook up an extra if you have one. they are cheap).
if the wires at the siren check out, then i actually agree with Pro. even when you know what you are doing, alarm troubleshooting can be daunting. find a shop you trust that will give you a free or cheap estimate.
and for what its worth, i do installs here and there so im no expert by any slight means, but if faced with a faulty brain and no warranty, i would get something new rather than even mess with the old alarm. the technology moves too fast. get yourself a nice lcd two way alarm-keyless entry-remote starter. DEI products are always highly regarded. (watch the ebay stuff. ahem, some of it is poo).
let us know what else you find out. good luck.