Hi Sue,
Obviously the veneer will have to come off. Depending on what you want to spend on this, you can either go cheap (leave it off and make the wood underneath look beautiful) or buy replacement veneer. The biggest problem with replacing the veneer is getting the old stuff off, but you seem to have had nature help you with 99% of the work.
Veneer in Australia is pricy but if you love your cabinet it's worth it. The veneer is the most difficult thing on a cabinet, too. They are very simple and easy to restore, and they don't have to be perfect if they're to be covered with veneer. Sometimes the other wood (drawers, I'm thinking of you) needs to be assisted with glue, but nothing hard and with either a traditional shellac finish (adds a beautiful orange tint) or polypropylene (very hard and shiny), it'll look like new. For the cast iron legs, enamel is a good option as Japanning would cost a bundle and there are probably no Japanneries in existence anyway.
The locks are almost useless so I'd just leave it, but you'll be able to find people on certain auction sites selling drawers with working locks.