Onan Marquis 5500 Model 5.5 BGMFA11578G

Try holding your dash "boost" switch when you try to start the generator. This will connect both the house and the chassis batteries to the generator starter circuit.

If you use the outside switch (the one on the generator)
Press STOP and hold, after about 30 seconds you (Gasoline gennies) will hear a CLICKING noise. hold till it stops. then hit Start.

If you hit start and it does not crank the suspect list

Notheing: Switch, battery, Pilot relay
Click but no clunk Pilot relay
Clunk but no crank, Starter solenoid/starter motor
Clatter Low battery
High pitched whine That is the bendix not engaging the ring gear.

In many cases a bad conneciton or battery will simulate a bad electrical part.

I HAVE TWO SIX VOLT BATTERIES AND I CHECKED THE INDIVIDUALLY AND THEY BOTH REGISTERED 6.7 AND TOGETHER THEY REGISTER 13.7.
THIS IS A GASOLINE ONAN GENERATOR 5.5 MARQUIS.
IT MAKES A RATTLING NOISE ON SEVERAL TRIES TO START AND THEN ALL OF A SUDDEN IT STARTS AND RUNS UNTIL I SHUT IT OFF.

Voltage for the battery has a lot to do with the starting process. You did not say if it was gas or diesel, maybe that does not make much difference however.

I know when my diesel gen. does not want to start I have to start the rv motor to help build up the batteries. That seems to help, also if diesel it will be common for that as it takes awhile for the glow plugs to heat up enough.

I third the ground cable/battery voltage.

Yup, what is voltage at the generator both before and while trying to start?

Check battery voltage, check battery cables (make sure you check ground ....both ends)