96ES 300 starting problems

I have a 96 ES300 with 335K miles on her. I have just started having this problem and wanted to see if anyone had a solution. When I go to start the car sometimes it will just click and not turn the engine all panel lights come on but no engine after a few tries the engine will turn and then be ok for a while and then same problem. At first I thought it was the battery but that has been changed and same problem. Any help or ideas will be greatly appreciated.