Replaced battery and lights work but won’t turn over

What is your question?

I jumped the car and let it run for about 20 minutes. I was going to run errands but before I did I decided to turn the car off and restart to make sure I didn’t get stranded. It wouldn’t restart. I tried to jump it again and lights came on but nothing. I thought the battery had a dead cell so I replaced the battery. When I connect the new battery the lights come on again but it won’t turn over. No clicking sounds or anything. I thought a fuse was blown so I checked the fuses that might be related to the not starting and none of them appeared to be blown. I also tried clicking the unlock and lock buttons on the remote to reset the immobilizer but it didn’t help either. Not sure what to do…

How long has your 2007 Lexus LS460 had this problem?

Started today