the key code light and fuel injector light stays on

I have bought a fiat brava (1.4 12v 1996) 3 months ago. The previos owner of my car installed alarm and the remote locking system in it. He gave me
2 keys and master key. I really like the car and I hadnít had any problems until.... Battery from the remote controller went off. I changed the battery, but the car couldnít start. I switched off the alarm, and then it started. The following day I turned on the alarm and all was working properly, except the sound signal of the alarm didnít working. A few times the car started normally. But once he couldnít. I switched off the alarm, and then it started normally. Later I switched the alarm on and the car started normally for some time. The the fourth day I started the car normally for the few times. I turned it off and tried to start it after 10-15min and it couldnít start. The key code light and fuel injector light stayed on. I canít start the car with none of my two keys. I can only start it when I input the electronic code from my code card. Then the car starts properly and works properly. But the key code light and fuel injector light stays on all the time. I went to Fiat service, they told me they can only change the computer, which costs a fortune. They are not of any help. Can someone help me, please? What should I try to do and in which order? Change the keys and code system or what? Remove the alarm away from the car? Iím quite desperate and would be very grateful for a help...
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