Dead drive. But check in another system to be certain.
Edit: When you say, "not recognized", do you mean,
1) Not showing up under the SATA devices list in BIOS
2) Not showing up under the boot devices list in BIOS
3) Not showing up in "My Computer" in Windows / File Explorer,
4) Not showing up in Disk Management?
It should at least show up in Disk Management, and allow you to prep the drive for use. If it does not, it is most likely dead.
Edit: There's no reason that a SATA6G (SATA III) SSD shouldn't work in a SATA2 or SATA6G system. Your system should be new enough that an SSD is no problem.
You might just be overlooking that a brand-new SSD is fully blank, no partitions or formatting, so you have to go into Disk Management to "prepare" it, it won't automatically show up as a drive letter in Windows / File Explorer. (Like most "ready to use" USB3.x portable external drives are set up, they are designed to be plugged in and data copied to it. Internal drives are different, and must be "prepared" before usage.)
Also, if you intend to make it your OS drive, look into using cloning software to move your existing OS installation onto it, and then physically swap drives, or make a Win10 install USB using MS Media Creation Tool, and a blank USB flash drive.