If the OS was installed with the HD connected, the bootloader (mbr) or boot partition (gpt) may have wound up on the hard drive and installing the hard drive back on the computer should make it boot, then use EasyBCD to repair the the bootsector making sure it's saved on the SSD. Then you can remove the HD.
Is it possible that the HDD had either the boot manager or the hidden partitions instead of the SSD? If so, you will either have to reinstall the OS, or put the drive back in.
If the OS was installed with the HD connected, the bootloader (mbr) or boot partition (gpt) may have wound up on the hard drive and installing the hard drive back on the computer should make it boot, then use EasyBCD to repair the the bootsector making sure it's saved on the SSD. Then you can remove the HD.