nuttable02lex, I have similar symptoms..Thot it maybe it was the battery or alternator so I had them both checked out at a garage..Alternator checked out fine, my battery was OK but near it's end so I had it replaced.
Im thinking about bringing my sc300 to the toyota dealer and have them take a look. Based on the feedback I got from everyone else and my own experience, I'm inclined to think it has something to do with either the fuel pump/filter or the ecu (which I think has something to do with the computer which regulates the flow of fuel).