I've done a little research and it seems like the problem may be the float being stuck. Is this a pretty simple problem that I can fix from home?

 

When this happened on my 04 Heritage, I removed the float assembly and cut the tip extension off the end, that gets stuck. Once done it will never stick again.

Run the fuel low, then take the console assy off. The float assy is a little tricky to remove, but just jiggle it and it will come out. Once out you will see on the end by the float a little tip that sticks out, just snip that off, and you will be good to go.

 

A loose or disconnected ground wire will cause that indications with many vehicles.