Starting problem Intermittant

Approximately 1 of every 10 starts the car cranks for a second like normal then fires, runs for 1/2 second then dies. If you try immediately to start it again, it will just crank but will not fire and run. You have to let a minute or two or sometimes more. 10 min. 20 min. Pass and then the car will start and run. This problem began 2 months ago when I used a different key to start the car. (I have 2 keys with chips in them that start the car- I keep one hidden on the vehicle. I also have a key with no chip that will open the door but not start the car). I left the key I normally use in my office so I opened the door with a key wired to the car that had no chip in it. I had forgotten it had no chip and when I tried to start the car it did not start. I then used the spare key with the chip and it would not start the car. It just cranked. I went back to the office and got the original key I always use and eventually it did start the car. So does the other key with the chip. I just tried it and it started and continues to run. Either of these keys have the same recurring problem although not consistantly. The other night after waiting 10-15 min. I finally pulled both battery cables for a minute and it started and ran. Whenever it malfunctions it starts immediately as always but only runs for 1/2 second and then quits. When trying to restart it, it only cranks. On a few occasions when holding the key in the start position, it will crank. Stop cranking, crank, stop cranking, crank. Until I release the key from the start position. I never had any issues prior to using the other keys not normally used. I also reprogrammed the second key by starting the car IMMEDIATELY after I started it with the original key. I am hesitant to take this to a shop as it is an inconsistent problem and not easy to diagnose. $$$$$ Please help. Thank you. Mike