Make sure your COM port is configured correctly, and that you have the baud rate set properly. (I believe all Xbees default to 9600-n-1 from the factory.) Then try using the "X-CTU" software, which you can download from dig's website, and use the button to "test/query" the Xbee. This will help you troubleshoot any cabling issues, and/or COM port settings. If that works you can use the "modem configuration" tab and have it "read" the settings from the XBee.
The first time I used an Xbee I couldn't get the +++ to work, and it ended up being the way i was typing it. You can't type any keys for a few seconds before the sequence. Also, the three '+' keys have to be pressed fairly quickly AND you may have to wait a second or two afterward (without pressing anymore keys) before you'll see the "OK" response.
Also - I believe that the LED on my series 2 devices blink, just like on the series 1's. So you may have an assembly defect on your adapter module. Double-check all the solder joints.
I hope that helps. If not post some pics, as I have several of these Adafruit Adapters, both real FTDI cables & the SparkFun FTDI/USB board, and several different type of Xbee Modules (series 1 & 2 in both standard and pro). We should be able to figure it out.
Cheers and good luck!!