To see whether SP3 for Office 2007 is installed, open Word, click the Office icon in the upper left corner of the Word window, click Word Options at the bottom of the panel that opened, and click Resources in the left column of the Word Options panel. The bottom item in that panel is "about Microsoft Office Word 2007". Immediately under that title, you should see Microsoft Office Word 2007, followed by a version # in parenthesis, and then followed by "SP3" if it is installed.
If it is not installed, it should appear in the list of updates the next time Windows Update runs. Or, you can initiate it by running Windows Update or by selecting "get updates" in the Resources panel mentioned above.
The diagnostics report you attached to your previous post seems to contradict itself. Near the top, it says it found no problems but then farther down, it mentions a possible hard drive issue along with some comments about SMART, the Self-Monitoring, Analysis, and Reporting Technology found on some hard drives. And then farther down, the report says "The Memory Diagnostic found evidence of failure in the random access memory (RAM)."
So, again, it seems to contradict itself. I'm inclined to suggest ignoring the report and just focus on your actual experience with the computer. How long does it take to get to the login screen when you start your computer? When you first open Word, how long does it take? When you close Word and reopen it, does it open almost immediately?
