The GX620 is a SATA-I with only one SATA port, but I didn't have to do anything special. I did reflash the BIOS to the latest version.
Do you have RAID enabled or anything else that might interfere with the functioning of the SSD? The SSD should be backwardly compatible with SATA-I; the same SSD model you have is working very well in my old SATA-I GX620.