You would only be liable to buy a new battery under the following conditions:1) The theft was due to your negligence; for example, you neglected to lock the car, or parked it in such a dangerous area that no reasonable person would have parked it there.2) You had agreed, when you borrowed the car, to be responsible for any losses, theft, damage, etc.3) You had borrowed the car without persmission.4) Or (obviously) you had conspired with someone to let them take the battery.But without either your agreement to pay for the battery, or you having done something wrong and therefore causing or contributing to the theft, you would not seem to be liable.