When you said the BIOS wouldn't recognize it as a bootable device, I assumed you were unable to install windows on the drive. Since you've been able to get as far as installing windows to the drive and booting the OS, I'm assuming that you installed the OS to the SSD, then it's clearly not an initialization problem.
If you have not been able to install windows to the SSD, which I'm still confused about since you mention a HDD and not being able to select the SSD, but then say it boots windows, then it's likely still an initialization problem.
What, EXACTLY, is the current configuration? Is the hard drive previously attached to the system still attached to the system? Has that drive been wiped of any existing boot partitions? If not, that's likely to be your problem as the BIOS may be reading multiple boot partitions or trying to use the partition tables from one drive to boot the OS on a separate drive. Just need to know exactly what is what.
Is the old hard drive still connected to the system? Have you managed to install the OS to the SSD? Have you booted the OS from the SSD? Have you checked to see if there are any BIOS updates available for your laptop? Hardware compatibility with newer devices is the most common reason for BIOS updates so I'd probably start there to see if any new firmware is available, both for the laptop AND for the SSD.
What is the full model number as printed on your laptop case either on the back or under the batter on the laptop case? The model you listed above is only a partial model number and does not in any way particularize your unit as the full model number does. There are about fifteen sub models of that laptop and they all have different hardware capabilities, configurations and BIOS firmware revisions.