Re: Error MSVCR100.dll
Is this on Windows 10? The MSVCR100.dll file is part of the Visual C++ packages. Yours is either missing or corrupted.
Try running a system file checker to find and fix any system file corruption: Windows key + X; choose Command Prompt (Admin) or Windows Power Shell (Admin), whichever is there. Type "sfc /scannow" without the quotation marks, press enter, and see if it can fix the missing dll's. After it runs, it will tell you if it found anything, and if so, if it fixed it.
Uninstall and reinstall both Origin and SimCity, running the installs "as Administrator". Set both SimCity.exe and Origin.exe to "Run As Administrator". Try running SimCity again.
If you still can't run SimCity after the scan, press Windows key + I to open the settings window; Settings > Update & Security > Windows Update > View Installed Update History > Uninstall Updates. Uninstall all of the Microsoft Visual C++ Redistributable packages listed. Reboot your computer, then go back to the Windows Update screen and "Check for Updates". Install all updates, reboot as needed, and try again.
Reply back to let us know if you got it running.