Yes they are supposed to rotate open so there is something wrong. This may help.
https://www.jaginfo.org/threads/how-to-repair-a-non-rotating-air-vent.13482/#post-267218
I have the icarsoft 930 reader for mine which is jag specific. A generic one may work depending on which type though at this point you have nothing to lose.
First thing Mike, check the batteries are in the correct way and the connections are not bent.
Reading the codes may show something as it is strange to have both fobs not working.
To give you a starting point it would be prudent to get the codes read. Is the car jerking/hesitating whilst driving?. A good check of the air hoses for any splits may help.😎
Hi Baz, I’ve not heard of one our cars being stolen in this way. That said I have 2 Faraday pouches, one for each fob. Well worth getting and they do work.😎