Why won't my harley run when I turn the throttle?

Fuel pump? It might not have enough flow.

there is a sensor on ur bike sometimes under the seat or around the battery box on the back of the sensor (always has two) it will look like plastic if that pastic looks like it melted they are the problem

This is caused by the ECU loosing or seeing an in-correct signal from the throttle position sensor (fly by wire). Remove the plug located on right side of bike mounted on the throttle body pointing towards rear of bike. Removal of air cleaner assy may be required. Spray a good quality switch cleaner in both the socket and plug. Allow to dry completely. Use HD contact grease in plug and socket to prevent this happening again.

i would also check at the the throttle body first that sounds like your problem. if that is not the problem it might be the fuel injectors i had almost the same issue. in 2006 and some of 2007 they claim they fixed the problem before 2007 bikes came out but thats not true. the angle that the fuel injectors sat was wrong they had to change the angle. how i fixed mine i installed screaming eagle injectors that sat at a 45 degree angle and never had a problem since. harley also had to pay for parts and labor. there is also a update or recall on 2007 harleys for a control module not sure wich one but call your dealer and ask them about it i know the module had something to do with the fuel or air i think.

Sounds like you're letting it idle too long with the enricher on. The enricher circuit is VERY rich and it will foul your plugs. When you start the bike, run the enricher only long enough to where you can get the bike to stay running with the throttle grip or throttle lock. Turn that enricher off as quickly as possible. Your plugs are probably fouled.

Good Luck
Steve

Possible cause is a crack in the fuel filter shell which is installed inside the fuel tank. Harley has a recall for affected models. Post your VIN number or go to your local dealer and ask him is there a recall for your bike. All he will need is the VIN number and any recalls will be done under warranty. By the way, not sure of the year of your bike but it may still be under warranty anyway. Other than that there could be a TP sensor fault.