The average attractive and useful life span of a rose is around 35 years - some can go on longer, if they've been fed and thickly mulched for most of their lifetime.
Personally, I'd get rid of it and plant something else - rose sickness may occur if you try to plant another rose in the same spot, but using a mycorrhizal product such as Rootgrow in the planting hole may stop that happening. Alternatively, take the opportunity to plant something different that suits the conditions and space available.
If you still want the rose and want to try to regenerate it, then yes, some drastic pruning back in spring is called for. You don't say where you are in the world, but in the UK, that kind of pruning would take place last week of February or first week of March. I'd remove the gnarly old wood down to about 2 inches, and any newer, healthier looking wood to about 8 inches. If you do this, you'll need to keep an eye on it to rub out any incipient growth buds which might be breaking in the wrong direction - you want new branches going away from the centre of the bush, not growing inwards, and nor do you want branches growing which cross each other and rub together later, so some minor, subsequent formative pruning may be necessary. It's also essential to make sure any sucker growth off the rootstock is removed - cutting back so drastically might induce the rootstock to produce lots of growth, which you don't want.
Whether you feed or not at that time is dependent on where you are, but certainly in the south of the UK at the end of March, I'd apply a specialist granular Rose Food, and top off with a layer of composted horse manure, making sure to keep it away from the base of the stems. Then it's a case of wait and see what happens - if it does grow again, most Rose Food instructions say to reapply 6-8 weeks later, so do that too. And keep up the usual spray regime as it leafs out, if it does.