My 4 cylinder Tiburon is having issues starting

My 4 cylinder Tiburon is having issues starting. It seems to start fine in cooler weather or in the mornings, but once it has been sitting in a warm sunny parking lot, it has trouble starting. This problem seems to happen at random, but more often during warmer/sunnier weather. When I turn the key there is no turnover, but all the accessories turn on fine (radio, electric windows, overhead lights). We also hear the humming of the fuel pump when the car is attempting to start. We checked the battery and it is fully charged. We thought that it might be a starter/ignition switch problem due to the heat affecting it. We changed the starter two days ago and it started fine that day (although my car was sitting in the garage most of the day and the weather was cooler and overcast), but yesterday it was having issues starting again (sunny/warmer weather). Do you think the problem is the ignition switch or something else?