I hope the lines aren't totally random. 🙂 As Juan suggested you want to make sure you are dealing with good geometry. I'll assume your problem is the lines have gaps that prevent polygons from being formed, and these are too large for the default tolerance to fix. ET Geowizards has several line tools and clean polygon tools you could use to close those gaps as well as the option to adjust your tolerance. I suggest you start reading the Build polygon, clean polyline layer and dangling nodes notes and then follow the recommendations therein. The gaps may be such that you have to do some manual fixing, but the Export Nodes wizard can at least point you to places where you have gaps.
Once your polygons are built then you have to get the attributes into the polygons. I'm not sure from your text where they are stored but check out a spatial join of either points or the lines to the new polys.