2001 hyundai xg300 won't start, faint click when I turn the key

check voltage at starter battery terminal when turning the key to the start position.

Check voltage on the starter terminal, same as answer #1.

Battery needs to be load tested! Charging system also needs to be tested! Why did you remove the battery cable while the engine was running?? That was a mistake! One of the easiest things you can do is try a jump start, with cables hooked up correctly. Just because a "meter" reads 12.6 volts means nothing as far as what load the battery can overcome! (hold and recover)

poss dirty battery cable or loose