At least based on dxdiag, It looks like the drivers are installed correctly. When you reinstalled them, did you try first uninstalling the old drivers from Ctl Pnl->Programs and Features. (if not you might try that as well)
As to your questions about the devices you're seeing in Device Manager
Are you really seeing an item titled NVIDIA High Definition Audio in Device Manager? I see Nvidia in dxdiag as your integrated graphics card (not sound)
fyi, for Hi Def Audio (which you have) connections are as follows (where Windows only talks to the Audio Controller. The Audio controller connects to all audio devices on the sound card)
Windows <==> Hi Def Audio Controller <==> Sound Card
Audio Controller
You should be seeing High Definition Audio Controller listed under DvMgr's System Device category (the code box snippet below is from your dxdiag report)
Code:
( Name: High Definition Audio Controller
Device ID: PCI\VEN_8086&DEV_293E&SUBSYS_02051025&REV_03\3&11583659&0&D8
Driver: C:\Windows\system32\DRIVERS\hdaudbus.sys, 6.00.6002.18005 (English),
Sound Card
The Realtek High Definition Audio Devices you see in DevMgr under Sound category are all devices located on the Sound Card
Also looks like the mic driver is installed OK as well so i don't have any other good answers as to your problem 
Code:
---------------------
Sound Capture Devices
---------------------
Description: Microphone (Realtek High Definition Audio)
Default Sound Capture: Yes
Default Voice Capture: Yes
Driver Name: RTKVHDA.sys
Driver Version: 6.00.0001.5802 (English)