Is the old computer still accessible (or a backup)? if so, you can move all your maps with this free program:
http://www.javawa.nl/gmtk_en.htmlOtherwise, if you are installing fresh from a download on this site, some maps suffer from an old bug in the installer. This used to work properly on old versions of Windows but it broke with Windows 7 64 bit. The problem is the installer does not create some registry keys that are needed.
There is a simple fix though, you just need to install a map that doesn't have this bug, it will create the registry keys needed for the others. Make sure you quit from Basecamp and Mapsource, then install this map. You don't need to use the map, just install it.
https://www.gpsfiledepot.com/maps/view/53/Now start Basecamp and see if the other maps work. If not, uninstall them with the control panel and re-install.