I need a cigarette lighter plug for my harmon kardon GPS, and I cannot locate the 800 number for harmon kardon.

Make sure your cigarette lighter works, try a different car. If it still doesn't work , your gps plug in ( charger ) needs to be replaced.

GOOGLE is your friend! Open up Google then search for this exact phrase (without the quotes)

"97 buick century cigarette lighter fuse location"

It's most likely that the fuse in the charger has blown. The fuse is located in the plug that goes into the cigarette lighter socket. On the end of the plug there's a ring. Unscrew the ring and it comes apart. Be careful not to lose any parts when you open it. You'll see the fuse which needs to be replaced. If this does not solve the problem it's possible that the cigarette lighter is faulty.

The plugs which are used with car lighters are often very poor; compare the firmness of the seating of the lighter with your accessory plug. The latter are often too loose to make decent contact.
Also, that plug is equipped with a fuse; unscrew the plug body and check the fuse.
I also recall someone having a failed plug on the Tomtom itself; it may be a weak point.

Found a cigarette lighter assembly that is the standard DIN/SAE size that is a direct replacement for the one in my car.

It sounds like you have a bad charging cable for the GPS or the cable is overloading the cigarette lighter.

The cigarette lighter is designed for less power then a 12v power outlet.

Therefore it is easy to blow the fuse for the cigarette light if you install something that draws too much power.

Fuse box should be located either in the glove compartment, or to your left below stearing wheel. Also check fuses under hood, should be located next to the battery. Double check the GPS, most of them will nox plug into cigarette lighter plug. It could damage the GPS.

Yes it does.

Buy a adapter for your cigarette lighter socket that has multiple sockets with one that will fit the Garmin adapter.
I've never heard of a problem you are having??
Are you using a Garmin plug?
If not get one.

You should be, Check to make sure the fuse isnt blown on either the cigarette lighter plug or in the plug that has the wires coming out of it.