I have a 98 TL and I've had starting issues ever since it was given to me a year ago from my grandmother, she couldn't figure out what was wrong with it either. So at the beginning when I'd go to my car to start it up, either it did or didn't just that simply and I was basically stuck. What I would find out later is if I let it sit long enough (like an hour or so) it would usually start. I got tired of that so I went to the junkyard and got a starter, put that one in but now I'd just clicking, but after turning the key multiple times it would turn over and start. I was told the solenoid was going bad which was the reason for all the clicking, but a new one cost $471, so I just ended up buying a brand new starter instead. The first starter I put in from NAPA would drag, but eventually start or just click, of course I took it back. Got another from advance auto, it start fine for a hot minute, then reverted back to the clicking again. So now I'm just totally stumped. Could it be the starter relay? I shouldn't be having the same problems after testing out two brand new starters on my car.

 

Check all of your connections. battery terminals, grounds, and the battery itself.
When it comes to remanufactured electronic that arent from the dealer, you get what you pay for. If you have a CarQuest near you, i recommend getting one from there.