I have a 2005 Harley-Davidson Road King (FLHR), while on a road trip the battery went bad; to get the bike started we pushed started it. After getting it started I found a Harley shop and had a new batter installed. After returning from the trip I tried to start the bike the next morning and found it very hard to start, I hade to thumb the starter about four to five times before the motor would fire, usually it would fire on the first try even from a cold start.
Question: should I have the ignition coil checked? Or the carb? I have checked the choke and fuel, all looks well.

 

check pos and neg conections , didnt state how far you rode with new batt. if any distance start checking charging sys.