Will not crank

I just replaced the starter and my van cranked up fine for only a day. Now I have another no crank, no start! Prior to replacing the starter, the car would start intermittently when I moved the gear shift up and down, not necessarily to neutral. After reading several posts, I was lead to believe my neutral safety switch may need repair or replacing. Then I read other posts stating if I hear a click, it is not the neutral safety switch. Not sure if that is correct, but there is a click when I try to crank it a single click at the new starter. Bottom line is the vehicle will not start now, with a new starter, even if I move the gear shift up and down or straight to neutral. The click is strong and the battery seems good; showed high voltage on meter. Also, the interior lights are bright and remain that way. I think the relay is good since the starter clicks, not sure. Possibly bad battery cables to the starter or bad negative cable? Main question is could it be the neutral safety switch even if I hear a click? Wanted to know before I removed the tire to test it. Also figured an Ohm test is best for this. Is this right? Thanks in advance for any help.