That is because it is NOT a clean install. It might be a NEW install, but it is not a CLEAN install. A clean install would include a new boot partition, which windows would create automatically during the installation if there wasn't one already present, which there was, since windows was previously installed on the other drive and you did not disconnect that drive when you installed. As we already said, you need to disconnect the other drive and install a fresh copy of windows on the SSD. At NO point during this process should the HDD be connected, AND it would be a good idea to use a partition manager to remove the "system reserved" partition that is almost certainly still there on the HDD.
You might be able to remove it in Windows disk management, but sometimes a third party utility is necessary as windows sometimes doesn't like to allow the removal of "system" partitions. The fact that you cannot boot the windows installation on the SSD when the HDD is disconnected tells me all I need to know about where the boot partition that's being referenced during POST is located, which pretty much has to be on the HDD.
Disconnect the HDD, reinstall windows using the EXACT method outlined above at the link I provided, and once the installation has completed THEN you can reconnect the HDD.