So this was my problem....sound familiar.....my Zumo 550 was would not run off of or charge for that matter off of bike power. I have a CAM Buss installed so I have power off the battery to the CAM buss, which has a fuse, checked the power at the leads going to the mount and I had power. NOTE: If you have a CAM buss installed....no need to check continuity on the fuse bc. you will not get a reading at the GPS leads if there is a short in the fuse. Anyway, so then I checked the wire from the CAM buss to the end of the wire that goes into the Zumo mount (a four pronged end that screws into the mount) and I had power. Then I checkd the pins on the mount (one will be power and you should get a reading if power is getting to the pins). I had no reading at the pins (gold nubs that the Zumo 550 sits on). So I cracked open the back of the mount and there it was.....a burnt track on the circut board staring me in the face. I am guessing that water or moisture got into the mount (I have had my bike and Zumo 550 out in some serious rain). Anyway, I would be willing to bet it is your mount. You can get it at Amazon.com pretty cheap...about $65.00. Don't get it direct from Garmin you can find it cheaper on the internet.
Read the rest of the thread and it looks like you have someother problem. Well anyway, here is my experience for anyone who reads this trying to solve a Zumo problem. Good luck on getting the problem solved.