Unwanted horizontal line

I have Excel 2003.

I have a continuous line under 7 cells, although only partly under the first and last cells. The line looks like a bottom border, but it is not because I cannot remove it with border formatting. If I remove the rows containing the line, the line jumps up a couple of rows. If I remove the columns containing the line, it's gone but so are my data and formulas. When I make a chart on top of the line, the line shows through the chart and when I copy the chart, the line comes with it. How can I remove this stupid line (which is now copied all over the place) without changing anything else on the worksheet? And also important, how do I avoid this happening again?

Thanks in advance for the tip, as my work colleagues don't know how to solve it.