I have no power to one of the switches no matter what position they are in and the lights do not work. I checked the main power box for loose connections, changed both switches, checked the bulbs, still no lights. The house is nine tears old, what happened?

Need voltage tester, start at switch box, Test, if 1 switch has power, the second should
Connect to first. Now test voltag out of switch, no power? Bad switch.
You situation may be different than this.

You should also check to be sure these are three way switches. Is it possible someone replaced a three way with a single not knowing what they were doing?

What do the switches control?

It is a dual control lightswitch for a light in our kitchen dining area and one for the overhead lights on my lanai. The kitchen light works but not the light on the lanai. There is also a dualswitch in the living room that controls the lanai lights and the ceiling fan on the lanai, the fan works from it's switch but the light doesn't from it's switch.

As Stratmando suggested, you will need a voltage tester to troubleshoot this problem. The may be a bad switch, even though both are new, a loose connection anywhere in the circuit from the switches to the light, switches may be wired incorrectly. Check the connections in the fan/light. Is there a pull chain switch in the fan? It may be bad, or may have been switched.

From above info sounds like the lanai may be controlled by 2 three way switches. I bet if you switched positions of other switch, then switch the one with no power, light may come on, If it does 3 ways wired incorrectly.
1 three way switch should have hot to dark screw, NOT the 2 white screws.
1 three way switch should have lite wire to dark screw, NOT the 2 white screws.
The 2 white screws from one switch connect to other 2 white screws at other switch with
2 wires(Travellers)Doesn't matter which.