Call a licensed electrician.

If it's the main breaker that's the issue, there's no way you should be replacing it without turning off the power to the house. Your electric company can check if you have any problems up to the meter.

From the description, one side of your 240 volt (split to 120 per side) line is either open or has a high-resistance loose connection. The problem could be anywhere from the pole transformer outside your house to your panel's bus.

Unfortunately, it's impossible to diagnose from here, and this is not something the average homeowner can troubleshoot without a good deal of fundamental electrical training and experience.

As for your main breaker not operating, I can think of a few possibilities.

It may be that you aren't actually operating the main breaker, but rather something else. (Your main should be clearly labeled. Presumably it isn't. Look outside, it may be there.)

Another possibility is a fault in the main breaker, which is uncommon, but a serious hazard.

The bottom line is that you need to get an experienced electrician in there NOW. Not somebody's brother in law, not some kid playing sparky with a phony license number painted on his truck, but a solid old-timer with knowledge and patience.

I know it's expensive. A house fire is much more expensive. Do it, please.