If the phone doesn't respond, you can't access the operating system - since there's no operating system to access. To make sure, as Shadow said, put a screwdriver through the memory chip, then work it around, so all that's left gf the chip is a space on the motherboard where the chip used to be. Or, if you've opened the phone enough to do that, just remove the motherboard, put it on an anvil and use a hammer to turn it into little pieces. (If you're really paranoid, use a propane torch to turn those little pieces red hot. Not even the NSA could read anything from the pieces after that.)
Don't microwave your phone unless you want an excuse to buy a new microwave. The frame of most phones is enough of an inductor to burn the magnetron in the microwave out before the phone even gets warm. You won't harm the phone at all, but buying a magnetron retail is almost as expensive as a whole microwave - assuming you know how to replace the old one without getting fried (or broiled from the inside, more likely). Even after the microwave is dead, there's still a large capacitor inside it that's charged with quite a few hundred volts, and it can supply a decent amount of current long enough to turn you into a memory.