Hello,
to identify the precise DLL file that is causing an issue, download a 32-bit version of the Microsoft Dependency Walker (http://www.dependencywalker.com/) and open arma3.exe with it. Then save the report from Dependency Walker to a file (File -> Save) and upload it here. I'll try to identify the file that is causing the trouble.

File : https://mega.co.nz/#!ZFhU0JIB!v37pFU9lyMtx3k1PafmBQUCaLrN_JRNgqmIAM98Cbmg

You have problem with these libraries: D3DX10_43.DLL, D3DX11_43.DLL (corrupted), OPENAL32.DLL (missing).

Run the Windows System File Check tool to repair corrupted/missing system files: https://support.microsoft.com/en-us/kb/929833 That should fix your problem.

I've made all the manipulations that you requested and nothing changed.

1. Then restart the computer.
2. Download and run DirectX setup from http://www.microsoft.com/en-us/download/details.aspx?id=8109
3. Restart the computer again.
4. If that doesn't help then run Dependecy Walker again and save and upload a new report.

File : https://mega.co.nz/#!8FgTkR4Y!oWHF85Y_-ut4FMvkok_QP-tF1PuSUSAPGo8cfcfZqYA

OK, so for some reason you have corrupted files that the DirectX installer can't fix.

I've upload those system files here http://arma.jiripolasek.com/files/FT24998_missing_system_files.zip . They belong to the "C:\Windows\SysWOW64" folder (beware that a different files with same name are also in C:\Windows\System32, but they are different version that is not compatible).