7-color RGB LED Help
Can you link to the item in question? If it was advertised as a "Blinking LED" then it's likely it is a small module that is set up to blink as standard (i.e. you don't have to toggle  power)  



If what you have is something like this Radio Shack Blinking LED then I think this may be the case. If you need to have more control over things then I would simply buy a standard RGB LED.

EDIT - just found this manual (actually written by someone who experimented a bit with them - the practically useless datasheet is here) with operation instruction linked to from one of the comments. It seems it can be toggled through various modes (including continuous on) by switching the mode pin to ground.
Here is an example circuit from the manual:



The "manual" says you must use a low enough value resistor to prevent the LED continually resetting. See the last page of the manual, apparently this happens when run under ~10mA, so make sure you are running above this.
It says on power up it should cycle through the colours 4 times then stop with red LED lit.  

I would aim for between 15mA and 25mA.
 The LED typical forward voltage is 3.2V, so if you are running it from a 9V supply and want 20mA, use a (9V - 3.2V) / 0.025A = 290&Omega; (270&Omega; or 300&Omega; will do)
For a 5V supply, you would use (5V - 3.2V) / 0.020A = 90&Omega; (100&Omega; or 82&Omega; will do) 

If it still won't work, post a picture/schematic of your setup with supply voltage and resistor value.