I replaced the starter solenoid even hooked a jump box to the battery and the mower will just click at the solenoid please help

Sounds like some were you have a bad ground

This is what I do: I use a simple 12V test light that you can get at the parts store for less than $5.00. I hook the clip to the negative battery post and then put the probe end on the places I want to test. First I go to the battery post side of the solenoid. I try to crank it and see if the light goes out. If not, I go to the starter post on the solenoid. I try to crank it again and see if the light lights up. If it does then the solenoid is working OK. Then I go to the post on the starter and see if it lights up there when I try to crank it. If all these work, then the wiring is working OK. If they don't then somewhere along the line we've found the place where it's lost connection.

Next, I unhook the test light clip from the negative post of the battery and hook the clip of the test light to the positive post on the battery. I put the probe end on the frame near where the ground battery cable is hooked and see if I have a ground there while trying to crank. If I do then I go to the actual engine and stick the probe right on the enging block somewhere to see if I have it there. If the light comes on all these times then it is probably the starter.