Steam - The Latest version of Microsoft DirectX(r) is required to play [game here]

If I try to launch any game from steam, it gives this error:

Steam - latest DirectX required
The latest version of MicrosoftX(r) is required to play [game] Microsoft DirectX(r) download site

However, I can still launch games outside of steam with the executable if that particular game allows you to (not all of them do, or some don't work properly.) This leads me to believe this error has nothing to do with DirectX 9.0c being installed, but something to do with the registry or incompetence on Valve's part.

This error is new as well, everything used to work fine. Tt's been happening for a month or so. I do not remember what I could have done that would cause this. I haven't messed with DirectX at all. I've looked at every search result I could find in regards to this error, but none of the solutions have helped.

The link in the error redirects to a page begging you to download windows 10 (guessing this is their way of saying Page Not Found.) I found the "improved" link to the download at https://www.microsoft.com/en-us/download/details.aspx?id=35&44F86079-8679-400C-BFF2-9CA5F2BCBDFC=1

As with Microsoft, installing fails with:

DirectX Setup: An internal system error occured. Please refer to DXError.log and DirectX.log in your Windows folder to determine problem.

But those two files are not in the windows folder.

Here's what I've tried (in no particular order):

• Reinstalling Steam
• Reinstalling some games in case it would download the needed DirectX
• Reinstalling the graphics card driver
• Reinstalling update KB2670838
• Reinstalling, from the control panel, everything related to .NET, C++, and Visual Studio
• Running the DirectX install as Administrator
• Using the "DirectX End-User Runtimes (June 2010)" installer instead
• Running them with steam closed
• Running them with anti-virus closed
• Running them in safe mode
• Running sfc /scannow
• Running CCleaner on the registry
• Launching game with /dx9 or /dx11

• Adding this to the registry:

  Windows Registry Editor Version 5.00
  [HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\DirectX]
  "InstalledVersion"=hex:00,00,00,09,00,00,00,00
  "Version"="4.09.00.0904"
  

Here is what DxDiag says

------------------
System Information
------------------
Time of this report: 1/2/2016, 18:08:06
   Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.151019-1254)
           Language: English (Regional Setting: English)
System Manufacturer: Hewlett-Packard
       System Model: p7-1247c
               BIOS: Ver: HIB_714.ROM vHIB7.14
          Processor: AMD A8-3820 APU with Radeon(tm) HD Graphics (4 CPUs), ~2.5GHz
             Memory: 8192MB RAM
Available OS Memory: 7664MB RAM
          Page File: 3754MB used, 11573MB available
        Windows Dir: C:\Windows
    DirectX Version: DirectX 11
DX Setup Parameters: Not found
   User DPI Setting: Using System DPI
 System DPI Setting: 96 DPI (100 percent)
    DWM DPI Scaling: Disabled
     DxDiag Version: 6.01.7601.17514 32bit Unicode

------------
DxDiag Notes
------------
      Display Tab 1: No problems found.
        Sound Tab 1: No problems found.
        Sound Tab 2: No problems found.
        Sound Tab 3: No problems found.
        Sound Tab 4: No problems found.
          Input Tab: No problems found.

--------------------
DirectX Debug Levels
--------------------
Direct3D:    0/4 (retail)
DirectDraw:  0/4 (retail)
DirectInput: 0/5 (retail)
DirectMusic: 0/5 (retail)
DirectPlay:  0/9 (retail)
DirectSound: 0/5 (retail)
DirectShow:  0/6 (retail)

---------------
Display Devices
---------------
          Card name: AMD Radeon HD 6550D Graphics
       Manufacturer: Advanced Micro Devices, Inc.
          Chip type: ATI display adapter (0x9640)
           DAC type: Internal DAC(400MHz)
         Device Key: Enum\PCI\VEN_1002&DEV_9640&SUBSYS_2ACD103C&REV_00
     Display Memory: 4074 MB
   Dedicated Memory: 497 MB
      Shared Memory: 3576 MB
       Current Mode: 1920 x 1080 (32 bit) (60Hz)
       Monitor Name: HP 2311 Series Wide LCD Monitor
      Monitor Model: HP 2311
         Monitor Id: HWP2939
        Native Mode: 1920 x 1080(p) (60.000Hz)
        Output Type: DVI
        Driver Name: aticfx64.dll,aticfx64.dll,aticfx64.dll,aticfx32,aticfx32,aticfx32,atiumd64.dll,atidxx64.dll,atidxx64.dll,atiumdag,atidxx32,atidxx32,atiumdva,atiumd6a.cap,atitmm64.dll
Driver File Version: 8.17.0010.1094 (English)
     Driver Version: 8.892.1.1000
        DDI Version: 11
       Driver Model: WDDM 1.1
  Driver Attributes: Final Retail
   Driver Date/Size: 10/24/2011 04:19:12, 862720 bytes
        WHQL Logo'd: n/a
    WHQL Date Stamp: n/a
  Device Identifier: {D7B71EE2-D500-11CF-CA77-C70ABEC2C535}
          Vendor ID: 0x1002
          Device ID: 0x9640
          SubSys ID: 0x2ACD103C
        Revision ID: 0x0000
 Driver Strong Name: oem130.inf:ATI.Mfg.NTamd64.6.1:ati2mtag_Sumo_Desktop:8.892.1.1000:pci\ven_1002&dev_9640&subsys_2acd103c
     Rank Of Driver: 00E60001
        Video Accel: ModeMPEG2_A ModeMPEG2_C 
   Deinterlace Caps: (truncated)
       D3D9 Overlay: Not Supported
            DXVA-HD: Not Supported
       DDraw Status: Enabled
         D3D Status: Enabled
         AGP Status: Enabled