Starter Problems in Honda Pilot

My 2005 Honda Pilot EX-L won't start. It drive it daily, and had driven it to my birthday celebration last night. After sitting about 4-5 hours parked, I tried to start it. It turned over normally, but did not catch. AAA attempted to jump the car and tested the battery, but did not find issues with it or the starter. I am looking for a reasonable idea what it may be, because the repair shop it was towed to doesn't have a great reputation, and I am a young woman who I suspect will look like a target for necessary repairs and high prices. I have just started working after a year of unemployment, so every dollar counts. Thanks so much for helping turn a birthday-gone-unhappy into a better ending.