agreed ^ you need a new battery.
either way if you change it yourself or get someone to do it the only main things to check out seem to be the alternator and the cables. your starter sounds fine to me.
most auto parts stores offer a discounted install and a free system service check with a new battery purchase.
For example: My car battery went flatline recently. Luckily this happened one morning in my driveway, so I had tool access and could use my parents cars to go get a new battery without stalling out on the way there. Anyways drove to Sears Auto...bought a quality DieHard Gold w/ 660 CCAs from them for 89$ Took the battery home, pulled the old one, installed new battery myself avoided any labor charge. Car started right up. Drove back to the store with my old battery. They then took 10$ off my bill for recycling the old one and while I was there I got the 10$ system service check for free. They inspected my install, checked my alternator and starter with their equipment in order to honor the warrenty on the battery.
