2005 Mazda 3 Car won't start sporadically

2005 Mazda 3 Two Wheel Drive Automatic 39,000 miles

I saw someone else post a question like this, but no one answered it.

I drove to work, car was fine, and when I came out 8 hours later, the car wouldn't start. Wouldn't make any noise, no turn over or clicking at all. I had it towed to my garage and the next day, they said it started find but did a diagnostic test on the battery (which is new) and the alternator and everything came out fine.

One week later, the same thing happened, but instead of wasting another 100 bucks on a tow, I left the car at my work and the next day tried to start it, and it was fine again.

I asked my garage guy why this is happening and he said it doesn't sound like the starter or anything else I suggested- but that it was an anti-lock chip problem. A chip that's in my key? Something is malfunctioned there, and to wait until it happens again and try another key? Does this sound right? I never heard of this before. I don't have automatic controls - everything is manual- windows, locks, mirrors. PLEASE HELP! I am afraid to drive my car again in fear of getting stuck somewhere.

Thanks