A low resistance across a capacitor (or any component) that is still in-circuit doesn't always signal a failed component. You're reading many components, perhaps, that are connected in parallel.
You can see the traces on the board. Use your ohm-meter to check continuity through the traces. If you find a failed trace (due to corrosion), re-establish the connection with some wire-wrapping wire (and a soldering iron, of course) from Radio Shack.
