Ignition key immobilizer problem
 

I recently purchased a 2002 Honda Civic, was all good for about a week. Then one day I went to start it, turned the key and nothing, as if the battery was dead. On the second attempt it started normally. Was good for a few days then did it again. Now it seems to be every 4th or 5th time I try to start it. A couple times it took several attempts before it would turn over and start. Every time this happens I see a green "key" idiot that flashes for a few seconds, and after I figured this out I would wait till it stopped before give it another try. I found some info in the owners manual, best I could do was ensure I had no other fobs on the keychain, which I didn't, actually only the one for the car is on it, no other keys.
Is the immobilizer the problem? Can I disable it?