Backup/Restore would help in this situation.
First on old laptop:
- Click 'Back up data' under top-left 'Accounts' menu.
- Select 'Back up to a Network folder' and 'Select a desired folder' location
- Click 'Back up now'.
- It should have created a backup folder of all the data. Copy the backed up data to a USB/external/network drive
Finally, on the new destop:
- Load the USB/external/network drive.
- Install ExpressAccounts,
- Click 'Restore data' under the 'Accounts' menu.
- Read the warning and click 'Restore from backup' if you agree.
- Select 'Restore manual backup' and 'Select the backup folder'
- Click 'OK' to restore.
Hope this helps!