Ambiguous Starting Issue

I have Honda Accord 2003 with 114000 miles on it. All of a sudden it started acting goofy while starting. It didn’t start for first few attempts, there was little crank in first 2 attempts. After 3 attempts, I waited for 1 minute and started and it started immediately,just like a new car. This behavior only happens if it gets cold (Florida weather cold) or I let the car sit for 3 days. I left my car at the dealership 3 or 4 times. They couldn’t replicate the issue. I changed the sparked plugs and got my fuel injectors cleaned and also replaced a gas pressure pump. I even got it towed and once car got at the store it started on first attempt. I asked them to change the air filter. Since then its working fine but during start up when I turn the key to start, it feels like car struggles to start but it always start on first attempts.

Can someone suggest if its a starter that is getting old?

P.s: Dash lights, Radio, Wiper and everything works fine on ignition.

How old is that battery? If it’s already 4 or 5 years old, I’d start shopping for a new one.