Bummer David,
Let's apply some KY common sense to see if we can get you fixed up.
1. If your bike works just fine with the petcock set to the PRI position, then your carbs are fine
2. If your bike will not run right with the petcock set to the ON position, and slowly runs itself to the point of dying, then you're running the float bowls out of gas. You have a gas flow rate problem.
3. When the petcock is in the PRI position the petcock allows for a gravity feed fuel flow to the carbs, when the petcock is in the ON position, an applied vacuum force is required to allow fuel to flow.
4. And since you also asked about "hoses", I am pretty safe to assume that you may not have the vacuum line for the petcock attached in both places properly.
Things to check;
Vacuum hose quality and connections between carb and petcock
Your oil for contamination (gas in oil)
Fuel filter?
You can test petcock vacuum operation by removing the main fuel line from the carb (leave petcock attached) and putting the end in a cup. Attempt to start the bike, if no fuel comes out, you still have a vacuum problem or a faulty petcock. Whenever possible, test one system at a time, combine working systems to create larger ones...
Hope it something simple for ya, and good luck!