What version of Windows is this on?
The online (shim) installer is the only Flash Player installer I'm aware of that returns 'Application Initialization Error' on occasion. The reasons are varied and I would need to get the online installer log files to troubleshoot the error. Please upload the Adobe_ADM.log and Adobe_GDE.log files saved at C:\Users\<YourUserID>\AppData\Local\Temp\Adobe_ADMLogs (Win Vista and above) or C:\Documents and Settings\<YourUserID>\Local Settings\Temp\Adobe_ADMLogs (Win XP) to cloud.acrobat.com/send using the instructions at https://forums.adobe.com/docs/DOC-7161 and post the link to the uploaded files in your reply.
ActiveX Control and PPAPI plugin are 2 distinct installers and one would not uninstall the other. What operating system is this on?
What Flash Player plug-in(s) is/are showing up in Add Remove programs?
What is the name of the PPAPI installer file that you used that uninstalled the ActiveX Control?
Please provide the FlashInstall.log file saved at C:\Windows\System32\Macromed\Flash. If this is a 64-bit OS, the FlashInstall.log file saved at C:\Windows\SysWOW64\Macromed\Flash is also required. Upload the file(s) to cloud.acrobat.com/send and post the link to the uploaded files.
Also, it sounds like you are in an enterprise environment. The online installers aren't meant for enterprise customers, as they are shim installers capable of including third party offers. Adobe offers a distribution license (usually free) for enterprise customers to distribute Flash Player (non-shim installer) within their organization. If you don't currently have a distribution license, I encourage you to obtain one at Adobe Flash Player Distribution | Adobe. The Flash Player Admin Guide also includes various distribution strategies for enterprise customers to deploy Flash Player within their organization
Windows 7 OS
Please provide the other requested information.