What SP version do you have installed, if any?
Please provide the Adobe_ADM.log file saved at C:\Documents and Settings\<YourUserID>\Local Settings\Temp\Adobe_ADMLogs by uploading it to cloud.acrobat.com using the instructions at https://forums.adobe.com/thread/1408375 or some other file sharing service of your choice that does not require a log in to access the file. Post the link to the uploaded file in your reply.
I have Sp2.
Thanks for confirming.
SP2 lacks the latest cryptographic technologies to sign binary installers, which the online installer uses. You can try the standalone installer posted at the bottom of the Installation problems | Flash Player | Windows 7 and earlier page in the 'Still having problems' section, however, there is no guarantee that it'll work. If it doesn't work, the alternative is to upgrade your system to something that supports the latest cryptographic technologies necessary to sign binary installers. You'll begin see similar behaviour (installers not working) with more applications as Microsoft will stop recognizing the validity of apps signed with the older sha-1 certificate in 2016 (see Security Advisory 2880823: Recommendation to discontinue use of SHA-1 - Security Research & Defense - Site Home - TechN…)