I have a 94 honda civic 1.6L 4cly. It quit on me yesterday and lost all power. Pulled the spark plug boots off and all 4 are full of oil! What has happened and is the motor finished??

wait it has oil in your spark boots it might be done unless you want to do a rebuild

Oil and not gas with carbon? You can have a coil go out and your engine die and find plugs fouled. You can get a multimeter and check to see if the coil is still good, or you can get a compression gauge and find out if the cylinders are done.

I was told that the valve cover gasket needed to be changed and that's where it's coming from. And I tested to see if it had any fire to it and it didn't. I was told the distributer??

Distributor is a good place to start. Make sure the cap doesn't have any cracks in it. Pull the cap, check the rotor to make sure it looks ok. You can take some light sandpaper and clean the contact on the rotor and inside the cap. The '94 Civic 1.6l has an ignition control module (ICM) which sounds promising, but I'm not really familiar with.