Display product with zero quantity?

I am using inventory control -- in fact, that is a major reason I'm changing from Paypal's shopping cart. I am currently out of stock of one of my items, but I want it to still show up and let people order it. What setting am I missing to enable this?

Admin->Configuration->Check stock level->false

Check stock level may work for you; another setting to change is Configuration > Stock > Products status in Catalog when out of stock should be set to (set to 1).

You also need to decide if you want to allow checkout when out of stock.

I already have admin - Configuration - Stock - Products status in Catalog set to 1.

If I make "check stock level" false, won't that disable all stock-checking? Will a sale still reduce my inventory level? What I'd really like to do is make some products able to be ordered with zero quantities and others disabled, but if it's all or nothing, I guess I'd rather have nothing as long as it will still track the inventory level of items.

FWIW, I think I fixed the problem. I had the "out of stock" button checked on the product. I changed it to "in stock" even though the quantity was 0 and it magically appeared.

Yes, that will do it to you...

To understand the options, the best thing to do is make some tests of settings and make test purchases (use check/m.o. payment). Create a dummy product for this if you want to avoid interfering with the real ones.