Clearly this is an old battery that can no longer store power. You do not mention of any lights in the dashboard. Go buy one.
check your battery cable connections. sounds like something is loose or corroded...
Could be a weak battery or and it could be going bad or even a alternator that isn't feeding it enough juice - Try checking the battery with a voltmeter and when it's revved it should should be putting about 14+ volts going back into the battery - Less it might be time to have your alternator checked.
Go to an auto parts store. They will loan you a tester to run out into the parking lot to test your car. Then they will sell you a new battery, which is what you need.
Check the grounds,
I started my car this morning, and it cranked very slowly before finally starting. I used the car throughout the day, and sometimes it would start slowly, sometimes start right up.
Then tonight after driving for about 40 minutes, I shut it off to go into the store. It was off for maybe 10-15 minutes, when I got back in and turned the key, there was nothing. No click, no chugging, no sound at all, but all the lights came on fine. Dashboard lights all on, radio worked, interior lights turned on without an issue and weren't dimmed.
After trying a couple of times, I was ready to call AAA and get it towed home, but decided to try one more time. This time it started right up. I left it running after this for about 15 minutes to see if it would shut off, and it didn't, as it also didn't throughout the day, so that makes me pretty sure it's not the alternator.
My question is, could this still possibly be the battery? Is it all possible for all the electricity in the car to work fine but somehow still not have enough juice to start the engine? Or does this sound like a starter issue?
