In the last week I'm having exactly the same problem with my 2003 GS430 and the battery appears fine.
It wouldn't start this morning on a couple of attempts, but on the third I turned it off and went straight from off to turning the engine over, instead of waiting on On for a few seconds, and it started like normal.
Where can I find the starter motor on my car to have look at it?
starter is in the middle of the V of the engine not east to get at need to remove the whole inlet manifold assembly not really for the faint hearted hope your problem is the battery or the solioid not sure if its a remote solioid but i will look tomorrow and post again