You need a license to watch or record, not to own the equipment capable of doing so.
Like it says on the TVLA web site: "It makes no difference how you watch TV - whether it's on your laptop, PC or mobile phone or through a digital box, DVD recorder or TV set - if you use any device to watch or record television programmes as they're being shown on TV, the law requires you to be covered by a TV Licence.
If you don't use any of these devices to watch or record television programmes at the same time as they're being shown on TV - for example, if you only use your TV to watch DVDs or play video games, or if you only watch programmes on your PC after they have been shown on TV - you don't need a TV Licence. If this is the case, please let us know."
It is perfectly acceptable to have a TV that is either not used at all, or only used for watching pre-recorded media or as a monitor etc,