1995 Dodge Intrepid Ignition problems

My Intrepid has an intermittent problem with the ignition. When the problem presents, the car will turn the starter, but not start. The dash lights seem to work, but the gas gauge does not show any gas and there is no sound of the fuel pump priming. You can turn the key for a couple of times and it does this, then the next time, everything works normally. The gas guage shows the proper reading, the fuel pump hums and the car will start after a normal turning of the starter moter. The shop can't make it do this, so they can't find the problem. What should I look for? How can I test for this?