I think you can solve your problem as follows:

If you insert a line in between each of your dataset in your worksheet and then make
sure that the "Connect line across missing data" is not checked you should get separate lines.

To add a new line in the worksheet mark the first line of data in the next dataset and select Edit->Insert
Go to the next set and repeat this for all your dataset. In case you have many worksheets to perform this action on it is probably not to difficult to make a scrip performing this action.

The "Connect line across missing data" can be changed in the "Page Control" dialog box, open it with a double-click outside the plot area in the graph window. (I am using Origin 5.0, i hope it is the same in your version).

Helge