My name isXXXXX am a Land Rover tech, as odd as it sounds you may just have a bad brake light switch. I replace 3 last week alone on LR3`s. The problem is, even after the switch is replaced the fault codes will have to be manually cleared with a computer.
Being a 2006 as long as you are under 50,000 miles roadside assistance will come tow the truck for free to your dealer or if you have the apco extended warranty it will also cover this.
There are only 2 diagnostic systems I know of that works on this truck and they are the Land Rover testbook of course and Autologic with the Land Rover software. Both of these are very expensive so not allot of shops have these. Most technicians should be able to replace this switch. Sometimes cycling the ignition key on and off 10 times will set the historic and not cause any problems, this is not a Land Rover approved method but works 50% of the time depending on the fault codes.
Let me know if I can assist more.
You are not going to have to replace the transmission.
Prices vary by region, here in central Florida at our dealership it would cost around $250.00 parts and labor for the switch and code diagnostics.
If the switch is replaced and the codes not cleared the only benefit would be being able to shift but the trans may not change gears properly and cause other problems with the trans.
You can try the key cycling like I described in the last post to see if that helps after replacing the switch. Maybe you could call around to some local shops and ask if they have the equipment to communicate this truck.
Of course the dealer is going to have the parts and software to expedite the repair so you can get to school on time and if your truck needs a software update during the repair they will have the latest patches available. My feelings is the dealer to be safe because I they have seen this happen on others so they know what to look for.