This forum is for SimCity 2013, not SimCity 4. If you post your question in the "Other SimCity games" forum, you may get some better answers. A couple of basic things to try: run in Administrator mode; make sure your antivirus or firewall are not blocking the program by adding the exe to the exception list; right-click the icon and disable Origin in-game; try running in compatibility mode (right-click icon; preferences; run as...)
Newer graphics cards and monitors can be a problem. The game was made to run on older monitors. Try forcing the resolution and turning off the intro movie via the command line. Right-click the icon, go to the end of the text box. If you have an HD monitor that runs in 1920x1080, add
"-CustomResolution:enabled -r1920x1080 -introff"
to the end of the command line; no quotation marks, make sure there is a space between the executable and the -CustomResolution. This post: https://www.gog.com/forum/simcity_series/simcity_4_tips_for_running_on_modern_windows/post1 had some more in-depth resolutions.