Strange you cannot install IRST, I've never seen that happen. It should be listed in Programs and Features, and have its own entry in Control Panel.
Try this driver directly from Intel, their latest for Z77 boards like yours, 11.7. You want the STOR_Win7_8_188.8.131.523_PV.exe file:http://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&DwnldID=22272&lang=eng&OSVersion=Windows%207%20%2864-bit%29*&DownloadType=
Or, Gigabyte has the previous version of IRST, 11.6, on your boards download page:http://www.gigabyte.us/products/product-page.aspx?pid=4440#dl
The Marvell SATA controller (third party) should not cause any problems installing the Intel driver. IRST will not install on the Marvell SATA chipset, but it can use msahci. Did you ever install the Marvell SATA driver? If not, Windows would automatically install msahci.
Frankly, given some of your previous posts, I suspect your SSD may be accidentally connected to the Marvell SATA controller. Start AS SSD, and just select all your drives one at a time and see what driver is displayed. If you see iaStor on any of them, IRST is installed, and your SSD is not on the Intel SATA interface. No need to run it, just select each drive to check its driver.
The Intel X-25M G2 was the first SSD I ever used, and I still have several of them. You can use the SSD Toolbox to secure erase your SSD if you need to, but back it up first.