ceiling light replacement - trouble

Help! I am trying to replace a ceiling light fixture which is controlled by a wall switch. The old fixture had was only a one-bulb lamp and had one black wire and one white wire.

The wireing from the ceiling outlet includes 3 white wires, 3 black wires, 3 copper wires, and one red wire. The way the original fixture was wired was - all 3 white wires were twisted together and spliced to the one white wire on the light; all 3 black wires were twisted together and capped off; and the red wire was spliced to the black wire from the light. The three copper ground wires were twisted together and capped off - no grounding at all!

My new light has three separate bulb sockets and is wired with one white and one black wire for EACH socket.
= 3 black wires, and 3 white wires

The problem. . . first I took all three ground wires and wrapped them ground screw on the mounting plate. Then I connected each ceiling white wire to a white wire on the light; then I connected each black ceiling wire to a black wire on the light. I capped off the red wire (I know, but I wasn't sure how to hook it up) When I turned
on the circuit, there was only one light socket that worked (with out the light switch, of course).

How can I hook up all of the wires so that the light switch will work?

 

Put all the black wires back the way they were before.
Put all the white wires together including the 3 new ones.
Put the three black wires from the new light to the red wire.
Put the ground wires all together with a short 4 inch piece sticking out of the connector.
Connect the short ground wire to the fixture.
You are not allowed to put more than one wire under a screw.