Probably the best course of action would be to boot to your HDD and after a successful boot connect the SSD to the system. I'll assume the system will be stable at that point. Then access the website of the manufacturer of your SSD to download/install their SSD diagnostic program. Virtually every manufacturer of SSDs has such a program available.
If the above is impractical or just non-workable, try the Hard Disk Sentinel for DOS program which will allow you to create a bootable CD from the downloaded .iso image. Hopefully you have a CD/DVD burner program already installed in your system so as to burn the .iso image to a CD and create the bootable CD.
The website for downloading the bootable CD of Hard Disk Sentinel for DOS is...
http://www.hdsentinel.com/hard_disk_sentinel_dos.php
If you don't have an .iso burner program available you can download the Free ISO Burner program from http://www.freeisoburner.com/
You'll be referred to another website for the actual download. Make sure when you proceed with the download you avoid selecting the garbage programs the download process will try to slip past you. I'm not sure if that's still the case with that program since I haven't used it in quite some time but I recall that was a problem area. Just download the Free ISO Burner program - nothing else.
So if you use the bootable CD just do so with only the SSD connected. The system should then boot to the CD without any user intervention. But if it doesn't, check the BIOS boot priority order so that the setting reflects a first boot to the CD. If the Sentinel program doesn't detect the SSD then shutdown, and also connect the HDD to the system (along with the SSD), and boot the CD to determine if the SSD is then detected and a report of its health is generated.