Does a wife become divorced by her husband's statement to her in a state of anger, "You are forbidden to me if you turn on the (receiver) again," along with him breaking it? Does she become unlawful to him by this, and is it permissible to install the device again?

It has been previously explained what the ruling is for someone who forbids his wife to himself: either he intends divorce, or ẓihār (a pre-Islamic form of divorce by comparing one's wife to a forbidden female relative), or an oath. The matter depends on what he intended. If he did not intend anything, then he must offer expiation for an oath (kaffārat yamīn).

Therefore, if you did not intend to forbid your wife and were unaware of the ruling, you must offer expiation for an oath if your wife turned on the receiver. If she did not turn it on, then there is nothing upon you.

As for reinstalling the device, if you will use it for beneficial purposes, such as watching Islamic programs and lectures, then there is no harm in it, along with the necessity of offering expiation for the oath. However, if you will install it to watch movies and indecent programs, then it is forbidden and entails danger.