RP's link to the schematic's is not working any longer so couldn't reference that source but sounds like your starter switch is the latest problem. First was when your battery went all the way down. Any time your battery is "killed" by leaving something "on" it will never be the same. Fix the starter switch first so that your headlights work when the ignition is on. Buy a new battery after that. Do you have a 12V test light? Very handy for tracing 12V and ground problems.
I know you have another Valkyrie to compare with so use another one for reference. If memory serves me correctly any time you short across the large connections on the solenoid the starter will turn. Be sure the bike is in neutral before you do this. All that the starter switch does is operate the solenoid and places that same short that you are putting across the two terminals. Any starter that I have ever had to deal with could be tested out of the vehicle by using jumper cables. Black to the case and Red to the 12V large terminal. Once you put the red to that terminal the starter will turn. You might have an open in the ground side of the circuit if your battery is known good and it will not turn when you short the terminals. I think you compounded your problem after the battery died by damaging the starter switch..................
Good luck. Keep this up Larue and you will be the Guru.
