If Lawbyte is running but without any data you are most of the way there.
On a single user machine the data resides in c:\program file\lawbyte\data and simply by copying the contents of that directory from the old machine to the new you will move the data.
However, a common problem is that a fresh installation of Lawbyte defaults to Practice No 1 and if your data has been set up under Practice No 2, at first glance it looks like you have no data. Try going in to Practice Maintenance on the Practice Menu, clicking on the drop down list of available Practices and see what you have. If you have multiple Practices simply select the live Practice and click OK, If there aren't any Practices there then we need to look at the data you have copied from the old machine to make sure it is actually real data.