What version machine were you running it on previously?
You can check on the SWX website and see what versions of SWX are compatible with what versions of Windows.
I highly doubt SWX 2007 is compatible with Windows 10 and there may be enough differences that it will not even work on Windows 10 in compatibility mode.
It also may be that the SWX system is 32 bit and the Windows 10 system is 64 bit and you would have to adjust for that.
Also be sure you are running the SWX application "As Administrator".
Ask your VAR for the activation part of your serial number (last 8 characters), maybe this information is also available from customerportal.solidworks.com. SolidWorks 2006 is the first version that can be activated. If you enter the 24 characters of your SolidWorks SN during installation, you should be able to use activation based license.
It might not work at all because of OS incompatibility as Todd Blacksher pointed out.