Why is my phone not restarting?

What are the indications, will it not even power on at all, or do it perform a "boot loop" where an animation just keeps running without end,...?

It sounds like you were overzealous in disabling Google apps, and may likely have disabled some system services and apps that are required to run. If you can't boot into Safe Mode, you may have to reboot into the bootloader and recovery (how will differ from one phone model to another) and perform a factory reset to default settings. You will lose some or all of your data on the phone when you so do.

I would not recommend disabling too many apps. If you don't want to use Google services, just don't sign in to a Google account. You can turn off certain Google account data from syncing by turning off sync in the Google account(s) screen. That way, for example, you can use Google Maps, but not sync any Gmail or Google Calendar information.