I think that the OP has been spanked (way more than) enough about leaving her purse in her car, so I'll skip past that. 
What I would speak to would be two things -
1) As already mentioned, I agree with having that car alarm checked and make sure you get it in good working order, so that you can depend on it; and
2) Some have mentioned (paraphrased) 'well, if a crook wants to break into your car bad enough, no car alarm or anything is going to stop them'. WELL, what I would say to that is that doing SOMETHING is a lot more than doing nothing. So there is no reason to leave your property more vulnerable.
Additionally, and as also mentioned here before, any deterrent is a good idea. They will go to the easier victims and pass you by if you do what you can do for your own best interest. This might not be true 100% of the time (there are always dumb crooks out there), but it's certainly a LOT more true than not true. 