Q: Relay failure

A few months ago, I took my car in to get an airbag replaced. They did something with the electrical system (I imagine to avoid setting the airbag off during the process) that reset my sterio and everything. When I picked it up a day later, I went to start the car and there was a delay between the time I turned the key and the start of the car. This continued for a few months. I took it in and they said they couldn't find the problem. A few days ago, the car died. It took a few tries to jump it, but once we got it into the shop, they said the battery was dead and the cables were corroded. On top of that, they finally found the source of the delayed start, and said it was the relay. Is there any chance they could have caused it?

My car has 52000 miles.
My car has an automatic transmission.