Breaking and then soldering back a flat cable, especially one associated with a fan, could indeed be related to why your MacBook Pro isn't turning on.
It may be because of short circuit, component recognition. If the fan cable is damaged or not properly connected, it could trigger thermal protection mechanisms that prevent the computer from starting to avoid overheating.
Your soldering job might indeed be the root of the issue, especially if it was not perfectly executed or if it resulted in a short circuit. Addressing these specific areas should help you determine if the fan cable issue is the cause of the MacBook's failure to turn on.