I have a rx330 2006 .It wont crank makes no noise and theres no sign of corrosion on my battery.

...well it isn't the battery...it's the end of the black cable that connects to the chassis/ground...unbolt that lug...wirebrush that lug (by holdin' it with a pliers) and the main automobile's ground with a wirebrush and put them together...make sure that the battery is younger than five at which point these tin/antimony alloy batteries will stop taking a charge ten percent per year~

I have a 2006 RX 330 as well, this has been the most frustrating experience. I have gotten the battery replaced twice within the last year. I'm still having issues as of this morning. I got mine jumped this morning, 20 mins later the car is shaking and then cut off and won't start again. No lights coming on unless I have it hooked up to the battery pack to jump my car. I read some other comments it could be a crank sensor or alternator. I have been to the dealership 3 times for them to tell me nothing they can see is draining my battery. Well something is I guess I will have to get it towed again today. Ugh