You need a licence to use any equipment capable of allowing you to watch or record TV programmes as they are being shown. This is ANY live TV, not singularly BBC programmes.
In theory if the equipment cannot record or display such programmes then no. If you have an analogue tv and there is no analogue signal available then you would be exempt from a licence as the equipment cannot display programmes as they are being shown.
If (for example) you own a set top box and that is used to run a sound only system (hi-fi for radio) and you have no equipment to display the picture then you do not require a licence.
With no available analogue signal your old tv will be little more than a monitor, therefore would not require a licence.
You do not need a licence to play dvds if the equipment is not capable of displaying or recording broadcasts as they happen.
Oh groan. Right, A television licence is required whatever the receiving system but if there are no analogue transmissons you would not need a licence for an analogue tv. If you still have an old 405 TV indoors it does not require a licence as you can't receive anything on it!!
Under the broadcasting act you need a licence to receive or record television programmes. That means ANY programmes not just BBC. If you could prove that you could not receive any BBC programmes it would make no difference. The licence is for the equipment to receive any broadcast television programmes. Reception of BBC is NOT a provision of licensing.
Yes, this does include set top boxes etc as stated elsewhere BUT set top boxes can be used without a licence if they are used for radio only and are not used in conjuction with visual display equipment.