I think you have five issues here, one of which is almost unimportant.
First, on many BIOS's, the labels used are odd, and they label a SATA HDD as an IDE which is Master of its port. So your screen shows that, on the SATA II port #1, it found an "IDE Hard Disk". This is merely a bad label, and you should ignore it.
Second, you do have a hardware problem to fix. The BIOS Setup screen you posted (I presume this is the new SATA unit) appears dead. Now, maybe it is faulty, but let's check on that first.
(a) Verify the the SATA port you connected to is Enabled.
(b) Verify that you have connected to it BOTH the power supply from the PSU and the data cable to the mobo SATA port. Check that neither is loose - some SATA data cables are prone to shaking loose.
(c) Did you change any jumper on the new SATA unit? You should NOT do that. (There is no Master or Slave setting to make on any SATA HDD.) If you did, change it back to the default setting as it came to you. (If you don't know it, check the maker's website). On some SATA units there is one jumper setting that makes the unit appear dead to most mobos, so if you set it that way by mistake, you have a problem. BUT if you never changed any jumper, then probably ignore this item.
(d) If the unit still appears dead in BIOS, can you try connecting it to any other computer to see if it also appears dead there? If you conclude the unit is faulty, contact the maker's Tech Support people to arrange a replacement.
Third (IF you can get the new unit to appear normally in BIOS Setup), you MAY have another issue to adjust. Now that you have installed your first SATA unit, the BIOS by default may assume that you want it to be the first boot device. However, it actually contains no data at all, so it can't do that job. Now, I assume you did not plan to work this way - that you plan to continue to boot from the old real IDE drive, and use the new SATA unit for data. What you need to do is go into the section of BIOS Setup where you select the Boot Priority Sequence and restore what you had: first choice is the IDE-connected optical drive, second is the older IDE HDD, and there is NO mention of trying to use the new SATA unit at all. If you make changes here, don't forget to SAVE and EXIT.
Fourth item depends a bit on which Windows you are using. Up to and including all versions of XP, Windows did not have any built-in device driver for an AHCI device (which is the real type for a SATA unit). Beginning with Vista, Windows does have that driver built in, so you can ignore this if that is your case. BUT if you're using XP (or older), AFTER you have the HDD working in BIOS Setup, boot Windows normally. The new unit still will not appear anywhere. But Windows should detect the presence of a new device, and load a driver for it. Ideally, this should be the driver exactly for your mobo's SATA chips, and that driver should be on a CD that came with your mobo. If you don't have that, go to the ASROCK website and find the SATA driver for your mobo and for the Windows version you are using. Once that is installed in your Windows, it will load automatically in future (just like any other device driver) so you can use the AHCI device. NOTE that you may read about installing a SATA driver in XP using the F6 key during a re-Install of Windows. You can ignore all that - it is only required if you plan to use that HDD as you BOOT device, and I don't think you are doing that.
Fifth, you'll have to Initialize your new HDD - that's a step ALL new empty units need. To guide you, read WyomingKnott's sticky at the top of this forum here:
http://www.tomshardware.com/forum/265764-32-guide-installed-disk-system
and pay special attention to his Step 5.