Right, if the symbols on your key fob are worn, are you sure you are pressing the right one? Sounds silly, but the ones on my wife's Citroen work in the opposite direction and I therefore get them mixed up, sometimes. (Please don't feel insulted).
Did you check the micro-switches in the fob when you changed the battery?
If you unlock the door physically with the key, does the alarm go off when you pull the door open? It should! Maybe someone has set the ECU or whatever so that the alarm does not sound when opened with the key.
When you changed the battery did you accidentally disturb, i.e. lose, the transducer, which is the thing that will stop the key starting the car. (Tiny little thing tucked into part of the key.)
If you have they key I am pretty sure there are ways of reprogramming the ECU so that you can open the car with the key and then get the engine running. People more skilled than me with the electronics, like Sierrafery, know about this stuff. They may get on this.
But I have played around with keys a bit because the push button bits wear out, simply and the innards get exposed to water ingress etc. You can get new key blanks and fob-cases off the internet very cheaply, I got a kit with two spare fob cases, key blanks, batteries and four new micro-switches for silly money. I transferred the circuit board to a new fob-case, but left the transducer in the old key. So they are both on the same ring, I use the new fob, nice and watertight and unworn, to open and close the doors, alarm and unalarm the vehicle, but the old key with the transducer, to start the car. Saved me having to have a key blank cut.
Really left-field this but is the car's battery, the main one, up to strength? If low, it won't operate the door locks, nor will it turn the engine over. Seems unlikely if the lights and wipers work, I realise. But this happens on one of my Disco 1s.
Anyway all the very best.
