Short answer: if a shop couldn't put it straight back on the shelf or rail today, it's not a donation — it's a recycle or a disposal, and taking it to a shop anyway just shifts your problem onto volunteers who then have to deal with it.
It's broken beyond use and can't be recycled. Never leave items outside a closed shop — it's treated as fly-tipping, and rain or animals often ruin things that could otherwise have been sold. See our full list of items charity shops typically can't accept for specifics.
Sorting a whole houseful of donate/recycle/dispose decisions at once, especially after a bereavement or big move? That's exactly what hands-on sorting help is for.