.... I took a look at the 96 Camry steering wheel pdf. On page 12, there is something called the steering lock mechanism. If nothing else works, I would probably see what is involved in checking out that part.:
http://www.**********s.com/camry/sr.pdf
It may be that you can remove the lock mechanism without removing the steering column.
There is also a solenoid that is involved somehow. Be sure this part is functioning properly.
.... clean electrical connections ... use contact cleaner spray.
Is it possible that you have blown a fuse that would affect the lock mechanism operation?
I would check first ....
... Let us know what you find out.