You don't need a new toilet, you have a clog
And the clog is most likely in the vent line.
I'm assuming that by "breather hole" you mean the tank vent thru-hull...if not, I need to know what you ARE calling the "breather hole" and how you "checked" it. Did you scrape it out? If not, you need to do that.
However, the vent thru-hull isn't only place the tank vent can become blocked...the other most common location is the vent line connection to the tank--both the vent fitting on the tank and that end of the vent line.
Before disconnecting the vent linee--or any other line in the systme, it would be a good idea to the deck pumpout fitting to relieve any pressure in the tank. Then remove the vent line from the tank and scrape out the fitting and that end of the vent line with a screw driver blade or whatever works.
Also look for any kink or sag in the vent line.
If there is no blockage anywhere in the vent line, there has to be a clog in the head discharge line somewhere. Do NOT use a plunger to clear it...plungers will damage a manual toilet pump. Do NOT use any chemical drain cleaner either. Which means that a snake is about the only thing you can use to clear it. But my money is on a blocked tank vent.
You might want to check out the link my signature...it goes to a comprehensive "marine toilets and holding tanks 101" manual that will teach you how to maintain your system to prevent problems like this.