If you're not sharing the same outlet with high powered electronics and the distance between the camera and the actual power outlet is not excessively far, then that would rule out a power issue. With the burning smell, that sounds like something has blown out on one of the circuit boards (fuse, capacitor, etc.)
If there's no kind of warranty on the unit, then you could always try taking it apart and looking at the internal circuit boards for dark/burnt spots. If you've got any soldering skills, it may be something you could replace. Or perhaps you could post some pictures of the internal circuit boards and someone here may be able to identify what has blown out and if it's something that could be easily replaced....Though my gut feeling is that repairing it, if it's even possible, would probably be more trouble than it's worth...Unless you're like me and enjoy the challenge of fixing electronics; Although with my eyesight not as good as it used to be and electronics becoming more and more compact/smaller, that once-enjoyable hobby is fast turning into a source of frustration.
