On the Schwinn I have, I took the chain off, the way frameteam2003 suggests to do (knocking a pin most of the way out). The chain was, as you describe, functional but crusty.

I soaked it in orange oil cleaner, then scrubbed it down with a wire brush.

Then I rinsed it in hot water, squirted it liberally with Simple Green, scrubbed it some more, rinsed it some more, dried it with a hair dryer, oiled it, and stuck it back on the bike.

I haven't gotten to ride it yet...I need to get brake and shifter cables and tubes and tires first, but running it by hand, none of the links seem to stick or anything.

If yours does seem creaky, however, it's not a big deal to get a new chain. Heck, you can even measure the new one against the old one. There could possibly be some stretch to your old chain, too. Mine was in good shape, just utterly, painfully filthy from 20+ years of sitting in a woodshed.