1996 Lexus LS 400 Car wont start period some days, other ti

The car sometimes just wont start at all -- the starter turns the engine fine, but it never kicks. That might happen at 7 pm in the evening -- can't start it no matter what you try. Leave it until morning, and it starts perfectly, as though there was never a problem. This has happened 4 times now.

In the last three weeks, it's started having problems after your driving. Everything is fine, starts fine, runs fine, then suddenly it starts hesitating, and it's difficult to get the RPM over 1500. I couldn't get the car over 10 mph going up a hill one evening. You press on the gas, and it almost kills, until you let off, then you get a short kick.

I took it to the local auto shop, and they kept it for 3 days, driving it all over the place, multple times a day -- and couldn't reproduce either problem.

No codes, no check engine light. Zip. That was three days ago. Yesterday, it started hesitating again (in the evening when they're closed). This morning it started fine, so I drove to work (no problems). Try to go home 8 hours later (75 degrees today in St Louis), and it won't start. Engine cranks, but no kick.

Lexus dealer looked at it 4 months ago after the first two events, and were unable to diagnose the problem.

Ideas? This is driving me crazy!