I have a similar problem, however, I bought the car with no remotes a few months ago. My Mother-in-law gave me a spare remote from her Holden Apollo (Australian badge swap of the camry ) to try and program to my car, but without a working remote, it doesn't seem possible/easy.
I am disappointed in toyota for this little bug in this series of cars because a dealer has told me the only way out is to buy a new system - bugger that!!! There has to be a cheaper alternative - and failing that.... it's an aftermarket alarm and a weekend of solder and side cutters. I would rather pay $100 for an alarm than $350+ for a genuine toyota one.
I'll keep you posted on anything I find.
Cheers
Shannon