hard to start, except when gas tank is full

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This started after I had to jump-start the battery, then replaced it which improved the condition. I then had my 60,000 mile service and it continued even though "supposedly" the fuel filter was changed. The mechanic said that no errors reported when he tested it. Now it has worsened except when the gas-tank is completely full. I am at a loss without more information and not sure what to do/where to go next. It sounds like it's trying to start normally but is rocking the engine pretty good until it finally turns-over. Any advice?