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What version of Mac OS X are you using ? Go to Applications folder and do you see Safari there ? If so, does it open from there ?
There are many reasons for this problem. It is possible that your Mac is infected with adware or could be corrupted Safari files. In Finder, hold down Option key, click on Go menu and select Library. Open Containers folder and move the com.apple.safari folder from there to desktop.
Then download and scan your Mac with this Anti malware application --> https://www.malwarebytes.com/antimalware/mac/
(You can download it from another browser or you can download it from another computer and copy the downloaded file to Mac and install it)
Then remove all malware or adware if it finds anything. Then open Safari while holding down Shift key and does it open ?
We need to run Malwarebytes to find and remove malware/adware if there is any. If there are any adware/malware, they usually result in crashing of Safari or prevent it from opening.
In Finder, hold down Option key, click on Go menu and select Library. Open Containers folder and trash the com.apple.safari folder.
Hold down Shift and open Safari. Does it open ?
If it is not opening, then go to System Preferences > Users & Groups. Create a test administrator account. Then logout from Apple menu and login to new account. Does Safari work in new account ?
No, AntiViruses won't do any good as this is not a virus issue.
Virus and malware/adware are different things. Adwares are browser hijackers and can affect them.
But there is a way. Open App Store, search Browser and download any free browsers. Then download Malwarebytes using this link --> https://www.malwarebytes.com/antimalware/mac/
Note : Malwarebytes is FREE for Mac.
Since Safari isn't opening from new account, that means it is not a issue with the preferences files. So it could be a malware/adware (browser hijacker) or the actual Safari is probably corrupted. There are some ways to fix it if Malwarebytes didn't work.
You can reinstall the OS X or you can update the OS X to latest macOS Sierra. Both procedure will replace old Safari app with new one. Let me know what you think.
If this is a 2009 or later iMac, then Sierra will work on it. Go to App Store, click Updates and you can find Sierra there. Download and install it from there.
Let me know how it goes.
Meantime you can download Chrome or Firefox using the browser you downloaded using App Store until we get this fixed