What does the engine do when it doesnt start?
Does the engine turn over but not start? or Nothing happens when you turn the key?
I take it, that this doesn't happen everytime. Just sometimes, yes?
It is the starter going bad. The old Toyota starters use a contact type solenoid that would produce a 'clicking' type warning when going bad. The fix for those was to replace the contacts inside. Like this..
Here's a video of replacing them on a Rav4 in the car...
The problem is that with the 2002 Camry, Toyota replaced that type starter with the reduction gear type and there's no contacts to replace. You just replace the whole starter and with that there is also no more 'Clicking' to warn you that the starter is going bad. It will just quite at random and then work again.
Please make sure the battery is good first.
Please ask more of me if needed.