You're original adaptor broke. You're replacement is either also broken, or not up to the job. Simples. Was the replacement cheap tat or genuine? I've seen cheap tat not put out enough power to turn on a TomTom regardless of what it said in the Ebay ad. Quick test to rule out a problem with your actual TomTom - do either of your adaptors power up another TomTom of the same/similar model (say a mate's)? You could, like you say, go for one of those cigarette lighter to usb socket adaptors and a standard usb lead, and you will either have the same problem again (if it's cheap tat only able to output <<1A), or it will work fine (if it's a decent one rated at >1A, up to 2A available these days).