So just to double check, the service in Windows is started but the following command in a command shell does not produce any output?
netstat -ano | findstr 10443
Did you customize the port for the inventory service? Fastest way to check:
HKLM\Software\VMware Inc.\VMware Infrastructure\Inventory Service\ in the registry.
If it is not customized restart the service and attach the following file to this thread or look for any exceptions in it.
C:\ProgramData\VMware\Infrastructure\Inventory Service\Logs\ds.log