there is either a bad connection to the solenoid or the solenoid itself is bad
Starter solenoid? Battery not fully charged?
Is the new battery well charged? Is the starter bendix stuck? Is the starter ring stuck?
Check your battery to see if it is fully charged and your wires are clean and tight. If so, you probably need a solonoid.
Possible battery, starter or connections/cables in between
if the battery and battery conections are good, then you need to replace the starter motor
starter, solonoid, ignition, battery. if it clicks when you turn the key then the battery is really dead or its the starter the battery could still be jumped if its the battery.
Weak battery or poor connection - battery to starter. Possible bad starter.
If the battery is bad, you may only hear clicks. It could be the starter, but I would check the charge on the battery first.
Typically this signifies that your starter motor has either jammed, or is faulty. To check that it has not jammed, give it a whack on the end with a small hammer, or fairly large wrench. If that does the trick, then the starter motor was jammed, if not, you need a replacement starter motor.
If the starter clicks, but doesn't start the car, that indicates that the starter solenoid is working, but the commutator that actually spins the engine is not. Take the starter back and have it tested. The battery could also be at fault. If the battery doesn't supply enough power you'll get the same result. check the battery voltage first should be 12.6 volts if not jump the battery see if it starts.if it does bad battery.
Seized engine? Weak battery? Loose or corroded battery cables? Defective starter solenoid? Flat spot on starter?
solenoids are what clicks, yes it will click if the battery is low.