I was discussing the issues surrounding the use of hearing aids on Shabbos with a close friend. One concern is whether one is allowed to speak directly to a person wearing hearing aids on Shabbos. Seeing my hesitancy to see any problem at all, my friend asked, "What if someone with a boom box on his shoulder sticks a microphone in your face? Are you going to talk into that? Huh? Huh? And isn't a hearing aid just a little bitty boom box with an itsy bitsy microphone? Huh? Huh?" Somehow the people I hang with tend to use such black and white m'shalim. (Often followed by a remark, usually by their wife who is rolling her eyes, "You have been hanging around Michael too much!" The 10 year old boy in me loves that; especially the rolling eyes and tone of exasperation.)
The root of the word "Shabbos" has nothing to do with resting. It means a cessation of certain activities which the Torah has revealed to us are fundamental to the creation of this world. By ceasing those activities, we testify that the world has a Creator. Be that as it may (and is), Shabbos certainly is meant to (also) be a day of rest. In order to preserve and enhance the experience of Shabbos, Chazal have established many g'zeiros, known as sh'vusim (plural of sh'vus). Not all sh'vusim were created equal, however.
First, there is "uvda d'chol", aka, "not in the spirit of Shabbos". For example, there is no issur to move your furniture on Shabbos, but to spend the entire day moving your furniture around is not likely to be very restful nor spiritually uplifting. Everyone know, however, that there is a lot of flexibility in uvda d'chol. Especially for parents who are trying to get a nap on Shabbos afternoon; anything that is either noisy or requires the participation of the parent gets labeled uvda d'chol.
Then there are real, live g'zeiros with real, live lists of detailed halachos. Muktzeh, for example. It's really assur to move muktzah (except under certain circumstances for certain categories of muktza, etc). Avsha milsa (things that are really noisy) is another g'zeira. Things that make noise draw attention. The issur of avsha milsa includes anything that makes a lot of noise, starting it on Shabbos would be forbidden, and the noise usually starts when the activity is initiated. That is, even if the activity was only set up to start on Shabbos -- so no actual m'lacha is done on Shabbos -- that activity is still forbidden. Setting up a time to start a washing machine or dish washer on Shabbos, for example, is included in the issur or avsha milsa. Lights on timers are not included; Chazal said noises that attract attention, not lights that attract attention; we don't make up nor even expand g'zeiros on our own.
So... the main issur with using a microphone with a PA system on Shabbos is that it makes a public noise (if it didn't it would be broken, after all). Hearing aids obviously do not fall into this issur, so you are permitted to speak directly to the wearer.
But they use electricity!!! Patience. In the meantime, feel comfortable talking to your hard of hearing friend. Lashon Hara, of course, is still forbidden.