If the flywheel can not be turned then likely the motor needs to come apart.----Water / moisture may have corroded the needle bearings well beyond economical repairs.
311126 is listed at 55 cents on one website.-------Something wrong with your information , I say.-----And what other trouble shooting have you done ?---I think your issues are far removed from this little hose !!----And it is NOT a vacuum hose.
Do a full inspection of the wiring cable from control box to motor plug in.------Control box is only to be used for motor functions.-----No instrument / radio / fish finder is to be operated from motor control box.
Some of us think that thousands of boat engines were damage in Texas.----Time to put your name on the list to get a replacement engine as there will be a high demand.----Or simply shop for a NEW boat.----Many boats will be on the market with cracked engines.
These motors do not need a battery to make spark !!----Post some pictures of the powerhead.-----It did not leave the factory with a charging system.----But a charging system was optional and could be installed at any time !!