Why does my Black Max generator, pm0497002 with a Honda engine only run with the choke closed?

https://www.repairclinic.com/Shop-For-Parts/a31b336c103/Black-Max-Generator-Alternator-Battery-Parts

Looks like a 12 volt. See the Werker battery on this page.

the chart shows figures of 10.7 hp-8.0kw with a torque of 19.5 ft/lbs- 26.4nm at 2500rpms ( max net torque)
the chart shows gx390 is 11.7hp (8.7kw) but the torque is the same as the gx340
you can get these figures from world. honda com or by going google and typing in--torque range of honda gx 340 motor at max rpms
10 hp engines running at 2500 rpms will be good for gensets of 5kw continuous out put as most makes run that size engine

GX390K1
Intake 0.15 +/- 0.02mm ( 0.006 +/- 0.001in )
Exhaust 0.20 +/- 0.02mm ( 0.008 +/- 0.001in )

Usually done with the engine cold/

I assume you refer to a 6500 watt Honda, if it's electric start/and manual(pull cord) First supply a 12 volt battery /if you haven't put fresh gas in it do the best you can to remove all the old gas from the tank and you should find drain screws and small hoses on the lower part of the carburetor. After completing this step add about 1 gallon or so of fresh gas, remove the air filter system from the face of the carburetor ,with a small squirt bottle put a tea spoon or so of gas into the of the carb, close the choke and turn the key, if it fires let it run with the choke closed for only a few seconds then slowly open the choke fully, if the engine stalls close the choke and start the engine again do not leave the choke closed for extended periods as this will cause engine flooding and spark plug failure. Also be sure you have inspected the existing spark plug to be sure it's clean if there is any question about the plug change it.

BR

replace spring apparently it lost its tension for it to stay open you may also have a dirty carburetor if it does not run smoothly with the choke wide open have it serviced or clean it yourself if your mechanically inclined it should be a piece of cake.

Linda, Sounds as though the engine is starving for fuel.

If you can access throttle linkage to the carburetor, slow the engine speed to idle before turning off. As mentioned in the previous answer ... turning off the fuel valve and letting it run dry is good if you are not planning to use it real soon.

Chokes are used to draw gas through the center jet to run. If the choke is not working properly and it is not closing all the way the engine cannot draw gas through the center jet and will not crank.
Your problem is just the opposite of that
Yours is getting too much air so that is why it runs only with the choke closed
You will see two set screws with springs attached to them. one is for fuel adjustment and the other for air mixture. Try adjusting the two in all the way and back off 1/2 turn each then try and start it. If not firing look at this website below and click on the video to view how to clean out the jet
http://www.lawnmowerman.tv/Videos.asp

Hi,
Most problems like this are a fouled inlet in the carb. Try adjusting the carb settings fully in - then back out tooriginal position. This often crushes any debris causing the problem.

Failing that, clean out the carb.

low oil sensor will not cause the motor not starting.
most likely is th ground wire.
you can try to attach that wire to any surface and try to start it. of it start, then you have to dis-assemble the head and find out where the wire should be attached.
if not, the wire is attached to a hot side. either way you have to dis-assemble the head.
http://www.honda-engines.com/engines_owners_manuals/ownersmanuals/gx390.htm
here is the site for the manual.