250 Mercury Outboard - Starts, Won't Run

We have a 2004 Mercury 250 Saltwater Outboard engine on a center console boat that we bought used. It had 120 hours on it at the time of purchase and we have added maybe 10 hours to that without any trouble. This is our first boat and we are learning as we go. We recently refueled for the first time and decided to take the boat to a local restaurant for dinner. Didn't happen. We had barely reached the channel and the boat died. Thinking the cold 2-stroke had flooded, we waited 5-10 minutes to restart. No joy. We did this several times before towing ourselves back to the house and driving our truck instead. The next day, we tried starting the boat again and it did fire, but it wouldn't run. First thoughts are related to fuel (filter, pump). What should we be looking for?