Praise be to Allah.
There is nothing wrong with signing up for high-speed Internet service (DSL) in return for a fixed monthly fee, whether you use the Internet all day or for just one hour, or do not use it at all, because it is akin to a rental contract for using the service for a month, and it is not stipulated that the user actually make use of it; rather it is sufficient that he is enabled to do that, and in that case he must pay the fee, even if he does not use it at all. This is like one who rents a house, and is thus able to live in it, but does not do so, or one who rents a car, but does not use it, and so on.
It says in Manaar as-Sabeel (1/294), explaining when payment for rental or hire becomes binding: If the rental period comes to an end, if it was connected to a specific period of time, then the item or property must be handed back, even if he did not make use of it.
And he said: If the rental period during which the item or property was at his disposal comes to an end, but he did not use it – such as if he rented a mount to ride to a certain place, there and back, in return for such and such a fee, and it was handed over to him, and enough time elapsed during which he could have gone there and come back in normal circumstances, but he did not do that – then it becomes binding upon him to pay the agreed-upon rental cost.
But this issue may be looked at from a different angle, which is that he is enjoined to be careful with his wealth, and it is forbidden to waste it. So if you have no need to go online for lengthy periods, and it is more economical for you to use other services that are based on being charged for the amount of time used, then that is more appropriate and is better, even if the link is slower.
There are those who are tempted by the availability of DSL service which allows them to go online for a long time when they have no need for that. This is a waste of money and is a waste of something more important than that, namely time. So you should beware of that.
According to the hadith narrated by at-Tirmidhi (2417) from Abu Barzah al-Aslami (may Allah be pleased with him), the latter said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “A person will not be let go on the Day of Resurrection until he has been asked about his life and how he spent it, his knowledge and what he did with it, his wealth and from where he earned it and where he spent it, and his body and how he used it.” Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
May Allah help us and you to do that which He loves and is pleased with.
And Allah knows best.