Firstly, have you verified that your SATA controller is enabled. Since you have an old system, it might have been set to default as disabled, since SATA drives were still an emerging market.
Trees is right, though.
Read this, from Wikipedia
Given the importance of backward compatibility between SATA 1.5 Gbit/s controllers and SATA 3 Gbit/s devices, SATA 3 Gbit/s autonegotiation sequence is designed to fall back to SATA 1.5 Gbit/s speed when in communication with such devices. In practice, some older SATA controllers do not properly implement SATA speed negotiation. Affected systems require the user to set the SATA 3 Gbit/s peripherals to 1.5 Gbit/s mode, generally through the use of a jumper, however some drives lack this jumper. Chipsets known to have this fault include the VIA VT8237 and VT8237R southbridges, and the VIA VT6420, VT6421A and VT6421L standalone SATA controllers. SiS's 760 and 964 chipsets also initially exhibited this problem, though it can be rectified with an updated SATA controller ROM.
The chipset in bold is the one that is used for your motherboard's SATA ports. If the drive does not have a jumper for 1.5Gb/s operation mode, you need to buy a new SATA controller card.
If the drive does have this jumper, set it to 1.5Gb/s so that your computer might read it. If it does, prepare the drive for your XBOX, and test it connected to the 360. Once you know its working, set the jumper back to 3.0Gb/s and connect it back up, etc.
Be sure to use the proper hdss.bin for your 250GB drive.