It sounds like the switch that senses the transmission is in reverse gear (for turning on the backup lights and the R on the dashboard) is stuck. However, that shouldn't prevent the engine from turning over if you have the clutch pushed in. If so, maybe it's a Toyota thing; I never had that issue with a manual transmission Dodge or Ford in the past. Call up a mechanic or the Toyota dealer repair department to find out what's wrong. By the way, it's also possible the battery is toast, or there is a problem in the ignition switch, starter solenoid, or starter itself.
P is for parking R is for reverse.
Normally you cannot take the key out whilst it's in anything but P
Could be something in the shift mech stuck. I'd try pulling a cable off the battery or if you are really brave a fuse and see if that resets it.
Otherwise, call the dealer.
Hello
That is because you should have been leaving it in P not R. It will not start as automatics must be either in P or N to start. This is to stop it being started in gear
Andy C
You said it is automatic, why would you park it in reverse? No matter I think your battery is dead.
I have a Toyota Yaris automatic. I always park it on an incline and leave it in reverse. I went to use it today and it won't come out of reverse! just beeps, flashes R and will not start up. i have turned it off and taken key out but it is still beeping!