95EXrocks

Bought this car about 6 months ago with 134000 miles on it. I put 250000 on my '89 Accord LX-i so I figured this one's probably got lots of life left in it. Anyway, after having it for about a month, I noticed every once in a while whe I tried to start it it would click but the starter won't roll the engine over. The lights are bright and the radio has plenty of juice. The last owner mentioned this problem and said she changed out the battery. She put in a cheap battery from Wal Mart (ugh). Even though it's a cheap battery I figure it should last longer than 6 months. Over time this problem seems to be getting worse and worse. I'm debating whether the battery is too weak to roll the engine or the starter is going bad. Once it starts this thing is rock solid. I do notice the gas mileage is a bit lower than specs. Replaced the air filter and spark plugs but that only helped a little. Was thinking about changing the fuel filter. What do you guys think?