First, start by making sure that your power source is OK. I know this sounds pretty basic, but it could save you time and money in the long run. Is it always on, or on only when the key is on? Does the lighter, a trouble light, or another device work when it?s plugged in there?
If it passes that test, then the problem moves to the power adapter itself. It?s common in many of these that there?s a fuse built in to them. A plastic ring surrounding the center contact can be unscrewed to get at it. However, the adapter that came with my TomTom is unfortunately not constructed that way. It's totally sealed. So if all TomTom adapters are like that, you?re out of luck. But since adapters are pretty much a commodity item, it could be that TomTom bought them from different manufacturers and yours just might have an accessible fuse in it. Check and be sure.
If you succeed in finding a fuse (and if it indeed is blown), get out a magnifying glass and read its current rating. It would typically be a number followed by the letter A. Then head down to Radio Shack or equivalent with the fuse in hand and buy a replacement.
One thing you always have to wonder when a fuse blows is Why? Sometimes it?s just a weak fuse, sometimes it?s something specific that you know to have happened, and sometimes it?s actually a symptom of bad problems elsewhere. So if the second fuse immediately blows, then it's probably time to throw the whole thing away.
If all this fails, then go to eBay and buy a USB adapter and a mini-USB cable. We are quite fortunate that TomTom chose an open standard for both powering the unit and connecting it to a computer. You can probably get both for maybe $10-15. Just study the TomTom end of the cable carefully to be sure it?s the correct shape, as there are a few different types of USB connectors. Another $5 or so will get you a right angle mini-USB fitting if that orientation is important in your installation. These are manufactured by Motorola for use with Razrs. Search for "angle USB Razr" (without the quotes) to find these.
Good luck.