I'd suggest adding 'nowadays' and changing people to 'we' to make the contrast clearer: Unlike many years ago when we could only rely on ordinary post office, nowadays cell phones help us communicate better with our families and friends.
The sentence, as a whole, doesn't make sense because you are comparing an object (the cell phone) with a time (many years ago). So, in this context, 'unlike' doesn't work.
If you changed the sentence to something like 'Nowadays we have cell phones to help us communicate with our families and friends, unlike many years ago, when people . . .' Here we are comparing one time with another time.