This error can occur after reinstalling or uninstalling some Windows applications. The AC1ST16.DLL is probably not missing, only AutoCAD cannot find it.
Go to Windows System settings of your computer and in the Environment variables, make sure that the PATH variable contains the folder name C:\Program Files\Common Files\Autodesk Shared (without the backslash at the end, you can remove it using the Edit button); maybe also stored in Program Files (x86).
If the file is really missing, you have to reinstall or repair your AutoCAD installation.
To set Windows environment variables, right-click on the 'My Computer' icon, select 'Properties'. In the 'System Properties' dialog, go to the 'Advanced' tab and click the 'Environment variables' button. You can modify the User- (for you) or System- (for all) variables.
(acad.exe or aclt.exe/acadlt.exe - unable to locate component)
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Please use these tips at your own risk. Arkance Systems is not responsible for possible problems that may occur as a result of using any of these tips.