As Barney would say: Nip it, Nip it in the bud.
He's 13, he's going to be driving soon. I don't know how you've handled punishments in the past, but I think you really need to drive home the trust factor.
You told him that he was not to move the TV back to his room, and I assume that you were perfectly clear on this point, and that he was perfectly clear on this point. He knew he is getting a similar TV for his birthday. Yet for whatever reason in his hormone addled brain he decides to move the TV you told him not to move back to his room.
That is a breach of trust. When you toss him the keys in a few years and he says he's going to the store and then he decides to pick-up a few friends and do some joy riding instead, what are you going to do?
If you don't punish him harshly, but fairly now for a breach of trust and failure to follow instructions, it's only going to get worse and potentially life threatening. Think of raising teenagers as training independent adults. You don't just toss the kid the car keys when he turns 16 and say "Good Luck", you teach him to drive and to follow the rules of the road. You let them take small trips and earn the right to have more freedom when they exhibit responsible behavior. This is no different.
If you don't teach him now that there are consequences to one's actions, and that privleges are earned, not entitlements, then you'll end up in 20 years wondering when this kid is going to move out of your basement.
He did something irresponsible, selfish, and disobedient. If it were me, I'd not only make him earn the money to get the TV repaired or replaced, but I'd let him know that there won't be any TV in his room for at least the rest of the year, maybe Christmas or his next birthday, if ever. It will all depend on how well he demonstrates to me that he is responsible enough for that privledge. I would make clear that his actions don't change how much I love him, but that because I love him, I am requiring that he earn the privledge of having a TV in his room. I'd give him a specific action plan of the types of behaviors and timetables that I require of him for chores to be done. I'd make sure he knew how to perform those chores adequately, and I'd inspect those chores once he'd done them to be sure they were done adequately.
Further, I'd insist that rather than paying him for chores around my house, which I'd expect him to do anyway as part of the family, he come up with some outside sources of income to make reparations for the TV, such as washing neighbor's cars, baby sitting, etc.
As for Grandma, if she wants to hire your son to help her out, God bless her and she can pay him to walk the dog, or whatever. I'd also let her know that I love her and appreciate her input, but make it clear that she raised me to be repsonsible for my own actions and expect that others are just as responsible. All you're trying to do is to raise a responsible young adult, who understands that actions have consequences, just as you were raised.
I agree that his damaging the TV was an accident, but it was the same thing as if he had agreed to run to the store to get milk and instead took a detour by his buddy's house and hit the light pole in the buddy's front yard by accident turning into the driveway, then got caught in a lie because he had to explain the damage to the car when he got home. Not that that ever happened to me or anyone I even know, ever. Really.
