Nick Adams, how did you try to install on your computer - using the files in the hard disk or from a CD or Download?
If you just try copying or moving it over from the external drive it will not install properly because it is looking for some of the files on the external hard drive.
Please let us know details of how you are trying to install and we can help better.
There is a method that I think will do it , but I have not tried it to change drives and it depends if you have all the installation files you will need.
If you go to the Windows Add/Remove programs and find the SolidWorks program, Right click on the Solidworks program listing.
then select the Change option.
This will open the installation Wizard and you can change the drive locations for all the different options from your external drives to your computer hard drive.
Be sure you have looked at every option to be sure that all paths point to your computer disk - not the external.
Then it will update / Change the install and put the files on your computer.
If this works, it may not delete the old files from your external drive - you will have to do that manually after you are sure everything is working correctly and you have copied all the files you need.
This method will only create the files required to operate SW - it will not copy or move any files you created and it will not retain any setting changes you made to the system options.
To save any changes you made to the system options, be sure to use the Copy Settings Wizard (in your windows program list).
if you install your solidworks in an external drive then i guess your license is embedded in your external drive.
when you install your solidwork in your computer does it succesfully?
if yes then if you try to open the solidworks, it will not open?