I guess you're suspicious that the problem is related to the immobiliser/key code just going by the way you've framed your question. A fair assumption if the key symbol on the dash doesn't go out as it should after a few seconds.
But before arriving at that conclusion maybe it is recognising the key but then staying illuminated because of a problem with a sensor or actuator in the engine management system. This problem is also stopping the car starting.
A good first step with such problems is to check wiring and plugs in the EMS loom. Not as hard as it sounds, pull out any plug you can find, clean contacts, smear with vaseline and replace (has worked for me when my 1.4 has started running rough). Check the idle control valve operation and maybe swap the injector for a scrap yard part.....a fairly cheap and easy job.
You can also do some more 'traditional' checks such as is there power to the fuel pump / is there a spark at the plug.
Also, if you're very lucky, simply disconnecting the battery for half an hour then reconnecting might work.
However, if it is just the car not recognising the key I can't help as it's not a problem I've had