Is the battery dead? Did you insert a new battery correctly? Is the hearing aid on? The easiest global check of the status of a hearing aid is the feedback test.
If you've ever put a microphone too close to a speaker (or been in the room when someone else has), you've heard the high-pitch squeal called "feedback." Put simply, feedback occurs when a microphone is able to pick up its own sound from a speaker. A hearing aid has both a microphone and a speaker, and sometimes this setup results in unwanted feedback (the "whistling sound you might have heard from a user's hearing aids). Incidentally, a quick fix for unwanted whistling would be to position the earmold more securely in the ear. Why? Because the properly-seated earmold will prevent sound from escaping from the ear canal that the hearing aid's microphone could pick up (the very definition of feedback).
The feedback test takes advantage of feedback by intentionally creating it for a few seconds. This is useful because if a hearing aid can produce feedback, it is an indication that the hearing aid is powered on, the microphone is able to pick up sound, and the speaker is able to output sound. The feedback test is a great way to verify that the hearing aid is powered on after inserting a new battery, unblocking the earmold sound bore, etc. Performing the test itself is simple: (1) lay the hearing aid in your open palm and there should be no feedback; (2) close your hand into a loose fist, and you should hear feedback. If you do not hear feedback during step 2, then the hearing aid is not functioning and you should begin troubleshooting.