I had the same experience with my 5 week old Legend Cx. Would not come on, either with batteries or plugged into the USb port. I called Garmin, and that has been a good experience. I had hoped that some magical combo of key presses would bring it back to life, but they said that was not possible. I mailed it in on a Saturday and got a new one back a little more than one week later. They included a note that said a faulty automoble power adaptor was to blame, and that I was to discard the current one and use the new one they included, but I don't have a car adaptor and have not used one. the last time mine worked was downloading tracks plugged into the PC. They also sent me a new usb cable, which I will use. I just now measured the voltage on the USB port on my PC, wondering if it was too high for some reason, and it read 4.8 V. I understand normal USB voltage is 5 V and the minimum acceptable is 4.4. My USB cable was hard to plug into and remove from the Cx. I am a little afraid to plug the new GPS into the PC, but must just go ahead and proceed since downloading/uploading waypoints, etc is necessary. BTW, the firmware version on this new Legend Cx is 2.5. I will upgrade to 2.6 again soon.
Good luck
Homer_AT