Electrical and charging problems

I bought this car on 07/06/2002, 2 weeks ago. I took it for a test drive, and it was all fine. After driving it for 2 days, the battery light and airbag lights came on. I then decided to replace the alternator. But the very same problem persists. I called a technician who tested all the wires and components, and couldn't find a fault. He said it might be the ECU. Now the car is completely dead and I'm thinking of cutting my losses and scrapping it. Any ideas?