Can I determine which of my two XBee modules is bad?

For the Series 2 (ZB) modules there is a setting that can alter or turn off the RSSI signal/light. Not sure about the S1 modules, so I'd check the product manual.

The other thing to try is restoring the factory settings via X-CTU.

If these are new modules and haven't been abused, chances of a bad one would be remote.