1998 Dodge Intrepid Possible Fuel problem

My car runs for so long then the lights so dim. After this happens, my check engine light comes on and it starts to cut out. If I push the gas peddle the whole way to the floor all the dash lights come on and the car will shut off. It can take an half hour to forty five minutes just to get it running then it will stop again. After several tries, it will turn over. I had it to the garage and they had it for three days. They claim that they ran my car around to areas that were 25 miles away and it did nothing. Could it be the coil, fuel filter, or fuel pump and why would my lights go dim right before this happens.