I purchased the three way Lutron dimmer switch at a big box store as well (I just read the question about the upside down switch problem); mine dims the light well. IF the other switch to the light is turned on, I can turn the power on/off from the dimmer switch; but if the other switch is not in the ON position, the light does not turn on using the dimmer switch. Please help.
Re-check that the correct wire is connected to the single-side of each switch. For one switch, that's the hot lead from main power. For the other switch, test the voltage levels on all three leads when the switch is removed. Two of the leads will alternate between 120V and nothng when you flip the other switch; the third lead is the output line and that's the one you connect to the single-side of the second switch.
There are lots of diagrams online, and most likely you can get a copy of the one that came with your Lutron switch at their website.
Sounds like the wire that is bringing electricity to the non dimmer switch is not connected to the common screw. This results in the light being controlled only in terms of (on/off) by the non dimmer switch. The dimmer will still dim the lights when the non dimmer switch is on but it won’t be able to turn the lights on. Find out which wire is bringing juice to the non dimmer switch and make sure to connect the “live” wire to the common screw, which is black and marked as “common” on most non dimmer switches.