1999 Toyota camery starting issues

Hi I have a 1999 toyota camery with 150000. Miles on it, 4 cylinder. Runs great but latly when its cold outside it wont start -- wont even try to turn over --but all the inside lights do come on --car makes no sounds at all after 3 or 4 turns of the key it starts like nothing is wrong recently serviced with a tune up - new plugs -batt check - and put on the computer all ok -- the car only does this once in a while but more frequently and im afraid I will get stuck somewhere. Can you help before I have to spend another 500.00 with no results. Thanks Jane :P